The question reads very differently if the word 'only' is dropped. The simple answer to "Does 1 Peter imply that we will receive salvation if our faith has been tried/proven true?" is "Yes, we will receive salvation if our faith has been tried/proven true." But to introduce the word 'only' into the question raises a very different issue, and not one that Peter raises, the answer to which is "No, they will not be saved only if their faith is tested."
The result (or, outcome) of tried and tested faith is what Peter is pointing out to Christians who had already suffered trials and testing of their faith. He is writing to encourage them to endure such trials because their faith is being refined and strengthened - purified, to have any dross sink to the bottom, as happens when gold is put through the furnace. However, he does not even suggest anywhere that unless their faith is so tested that they will not be saved! That is an entirely different matter, which would necessitate use of the word 'only'. But nowhere does Peter say "only" as in 'You will be saved only if your faith is tested.'
How could Peter even suggest that, knowing that the repentant thief on a cross next to Jesus was assured of Paradise within hours of his imminent death? How could that evil-doer have his new-found faith in Jesus 'refined' when he was unable to do or say anything further in the few hours of life left to him? What further, or greater endurance with regard to faith could possibly happen to him? He was at the ultimate end of his faith within two or three hours of having expressed it, to Jesus' satisfaction! Did Jesus say that, if he kept his faith until his dying breath, then he would be assured of Paradise? No! Jesus promised the evil-doer Paradise at the moment of his repentant expression of faith in Jesus.
Why is that simple fact overlooked by those claiming that we have to do certain things in addition to expressing faith in Christ? Why is Acts 15 also overlooked by such ones who say more is required for salvation than putting faith in the finished work of Christ? Peter was also involved in that Acts 15 crisis in the church, when some believers were trying to insist that for Gentiles to be saved, they must get circumcised and keep the law of Moses. Peter stated:
"Men, brethren, ye know how that a good while ago God made choice
among us, that the Gentiles by my mouth should hear the word of the
gospel, and believe. And God, which knoweth the hearts, bare them
witness, giving them the Holy Ghost, even as he did unto us; and put
no difference between us and them, purifying their hearts by
faith. Now therefore why tempt ye God, to put a yoke upon the neck
of the disciples, which neither our fathers nor we were able to bear?
But we believe that through the grace of the Lord Jesus Christ we
shall be saved, even as they." Acts 15:7-11 A.V. [Emphasis mine]
This is the same Peter, who years later, wrote to more Gentile Christians saying they had already been begotten by grace (the new birth) and had a living hope (present tense) because Jesus had been raised from the dead (past tense). (1 Peter 1:1-3). He adds that their incorruptible inheritance is reserved (present tense) in heaven for them, and that they "are kept by the power of God through faith unto salvation", (present tense) which salvation will be revealed at the very last (future tense) (vs.s 4-5) - when Christ appears.
Then come the verses you ask about. But given what Peter has just assured them of, it is clear that he is encouraging them not to be disheartened at continuing persecutions (trials) because those will only serve to strengthen their faith. And all the while that Christians endure trials, that serves to glorify God and Christ.
There are no exclusion clauses in what Peter says or writes. There is no hint that their salvation has a proviso attached - "Only if your faith is tested will you be saved." That simply is not there.