No, it verifies the time of His coming. But, it does impact the traditional teaching of men who have misplaced the time of the Lord's coming which was prophesied from the OT, and was imminent for those living in the first century AD. The Bible never uses the phrase "second coming" anywhere in the scriptures. That phrase is an assumption of man, and a false teaching.
It is derived from a misapplication of Heb. 9:28 which is often taken out of context.
"26 For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself.
27 And as it is appointed unto men once to die, but after this the judgment:
28 So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation." (Heb. 9:26-28, KJV)
The context of these verses speaks of Christ's appearance at the "end of the world" to put away sin by His sacrifice. When was He sacrificed? The answer is obviously the first century AD, as I believe in 31 AD, but others will say 30, or 33 AD. However, as His sacrifice was to put away sin, and as it happened in the first century AD, then the phrase "end of the world" is misleading.
The ASV translates it as the "end of the ages", as does the CJB, the ESV and the NKJV. The NET uses the "consummation of the ages"; the NIV has the "culmination of the ages", and the YLT has "at the full end of the ages".
An "age" was ending, and that age was the Mosaic age, and the age of animal sacrifices at that temple in Jerusalem (John 4:21).
Men have assumed this phrase to depict the end of all time, and literally the end of the entire world. But, that cannot be the meaning when the words are kept with the context of our Lord's sacrifice - "once....hath he appeared to put away sin".
The phrase "second coming" is not used. The words are "second appearance", and only those who had a first appearance of the Lord, those who had seen His first appearance, to those who had walked with Him, touched Him, witnessed His crucifixion and resurrection... those of the first century AD. They were the only ones who could have a "second" appearance of Him. No other generation has visibly seen Him even one time.
So, the phrase "second coming" is terribly and wrongfully misused.
The time factor has to be considered. As His second appearance was not going to be for the putting away of sin, then we know that His first appearance was to deal with sin. As His first appearance / manifestation (1 Pet. 1:20) occurred in the first century AD, then those of the first century AD were the ones who would see Him the second time. As His first appearance dealt with the sin issue, His second appearance would be for their "salvation" or better, their deliverance from persecution, their rescue.
Now that we can place the time of His second appearance in that same generation of those first century AD saints, then Matt. 10:23 makes perfect sense. His disciples would not finish their mission to all of the then known and existing "cities of Israel" before the Lord's return.
As His return was promised to them of that generation (Matt. 24:34), then His return was not to end the entire world, nor to end all time. The end that was prophesied from OT scripture was the "end of the desolations of Jerusalem".
Daniel's prayer in Dan. 9:18-19,
"18 O my God, incline thine ear, and hear; open thine eyes, and behold our desolations, and the city which is called by thy name: ...for thy city and thy people are called by thy name." (KJV)
The context of Daniel's prayer was stated in Dan. 9:2, in the second year of the king Darius, of the second gentile world power (Medes & Persians) of the image Daniel had interpreted for Nebuchadnezzar in Dan. ch. 2 -
"...that he would accomplish seventy years in the desolations of Jerusalem." (KJV)
Gabriel appeared to Daniel, and stated the purpose and time and people in Dan. 9:24.
"Seventy weeks are determined upon thy people and upon thy holy city, to finish the transgression, and to make an end of sins, and to make reconciliation for iniquity, and to bring in everlasting righteousness, and to seal up the vision and prophecy, and to anoint the most Holy." (KJV)
The prophesy was for Daniel's people - the Jews who returned from the captivity - and for Daniel's holy city - Jerusalem. The time was in the same context of Daniel's prayer for the end of the desolations of Jerusalem which he had found in Jeremiah's books, and which Gabriel corrected for Daniel.
The end of Jerusalem's desolations would not be upon their return from Babylonian captivity but the "end" would be seventy sevens of years - 490 years. Daniel thought he had been asking for the end of the 70 years of captivity, but the way he expressed his prayer to God was for the "end of the desolations of Jerusalem", and God answered the question Daniel asked.
The end of the desolation (destruction) of Jerusalem was defined in Dan. 12:7.
"...and when he shall have accomplished to scatter the power of the holy people, all these things shall be finished." (KJV)
Within the same prophesy that had begun in chap. 9, and for the same "holy people" defined in Dan. 9:24 - the Jews - when the power of the Jews were scattered then "all these things" of the prophesy from Dan. 9:24 would be finished. All of those things spoke of Christ's putting away the transgression of the Jews, to make an end of sins - that is the animal sin offerings that became profane once Christ was sacrificed, and the bringing in of everlasting righteousness.... all that began at the cross of Christ and was all finished at the destruction of Jerusalem.
None of those things which Gabriel told Daniel would go beyond the scattering of the power of Daniel's holy people, which happened in AD 70 at the full destruction of that temple... the culmination of the Mosaic age.
The "end of the world" was not the end of the entire earth; but it was the end of their world as they knew it, the end of their world which had revolved around that animal sacrificial temple in Jerusalem which had become profane once Christ was sacrificed on the cross.
So, Matt. 10:23 fits perfectly within the time frame of Christ's second appearance in that generation of the first century AD. But, it was not His "second coming", because He has "come" in judgment of both the world (Gen. 6-7), and nations (Egypt, Babylon, Israel, Idumea, Tyre, Assyria, etc) many times before.
A "coming" means the presence of the Lord, the people feeling His presence and seeing the outcome in the results of His judgment against the wicked.
"7 Yea, the stork in the heaven knoweth her appointed times; and the turtle and the crane and the swallow observe the time of their coming; but my people know not the judgment of the Lord." (Jer. 8:7, KJV)
God's "coming" was a time of judgment against the people, and the destruction of Jerusalem was a time of judgment against those wicked who had crucified the promised Messiah, the promised Savior. But, it was not His second judgment coming, as there had been many times of judgment before, and there have been many times of His judgment of wicked people since.
Time... the time factor is important.
For more on the time of His coming in that generation, please see the posts at my blog (Shredding The Veil), especially the ten parts of It's Not The End of The World, the eight parts of The Signs of Revelation; Daniel and the End Times; the seven parts of Frequent Mistakes, and the three parts of The Signs of the Feasts. You might begin here.
All bold emphasis is mine.