Yes, and Yes.
As you know, the New Covenant shortly followed. Pentecost was the day when the New Covenant was declared to the Nation of Israel. (It was the EXACT SAME DATE in history that the Old Covenant was declared to the Nation of Israel on Mount Sinai.) In other words, the theocracy in the Old Covenant (and New Covenant!) began on the day when God made his "tabernacle" among men on earth.
In the New Covenant, Pentecost therefore marks the first day that God made his "tabernacle" among men on earth by indwelling the bodies of believers. What unfortunately happened in the Old Testament was that the Shekinah Glory had departed Solomon's temple shortly before the Babylonian captivity. (Thus the visible theocracy on earth ended, and the "Times of the Gentiles" had begun, since Gentile world powers from that point forward would command the world.) It was during the Babylonian captivity that the prophets wrote extensively about the New Covenant, which was couched in terms of the visible (political) redemption of Israel. For example, when the people cried "HOSANNA!" to Jesus as he entered Jerusalem on the foal, they were expecting him to deliver (or save) them from Gentile rule, since the son of David would fulfill Psalm 2 (among other passages in the Hebrew Bible) to rescue the nation. (Hosanna = "Save us," and of course the palm branches were a clear reference to "tabernacles", when God came to man in the desert on Mount Sinai.) So let me emphasize again, the prophets during the Babylonian captivity (Ezekiel, Jeremiah, et al.) painted a picture of the New Covenant that had included political as well as spiritual redemption. So there is this expectation in the minds of the faithful remnant that the New Covenant will include the visible re-establishment of the theocratic kingdom on earth. That is why the disciples asked Jesus about the re-establishment of the visible theocratic kingdom on earth.
What happened was that the New Covenant was established WITHOUT re-establishing the visible theocratic kingdom on earth. To help describe what I am saying, please see below.
This graph is my own personal rendition of my own understanding of the Kingdom of God on earth as it relates to the Jewish expectation of a literal Messianic kingdom on earth. Again, we are not looking through a microscope, but taking a macro view from 30,000 feet.
Essentially, Jesus was telling his disciples to wait until Pentecost, when the New Covenant would be announced. (The "Times of the Gentiles" would therefore not end!) The Kingdom of God would be literal, but also invisible. In my "opinion", the prophecies in the Hebrew Bible will be fulfilled yet future, and therefore I believe the reference of Jesus to "the times and seasons" in Acts 1 is to what I have tried to depict on my graph -- i.e., the postponement of the visible theocratic kingdom on earth until the invisible kingdom of God on earth ("to the farthest reaches of the earth") is consummated. At that time, "all Israel will be saved" (Romans 11:25). When Jesus will deliver Zion, he will have removed ungodliness from Jacob (Romans 11:26), which is the purpose of the tribulation period (i.e., to remove ungodliness from Jacob). At that time, the New Covenant will be restored to the Nation of Israel (Romans 11:27). From that point forward, the VISIBLE theocratic kingdom will be established on earth, and the temple then will be occupied by the "Glory of the Lord," whom Ezekiel equates with the Shekinah Glory. Of course that Glory is Jesus the Christ.