The answer depends on the USTA Section because each Section is given the ability to handle disqualifications differently. It used to be that self rated players that struck out had all of their match scores reversed. I believe that is still the case in my USTA Section (Pacific Northwest). However, players with ratings based on NTRP tournament play or mixed doubles league results from the previous year, or those that had successful appeal (including medical) only have their last match reversed if they strike out. Therefore, if the player had an A, T, M, rating, and the Section where this player was from only disqualifies the last match, then his team would advance. If he was self rated, all of his matches could possibly be reversed, but the championship would likely stand because he team would have won 3-2 even after his DQ.
The FAQ's found here could shed some light:
FAQ #27 states that each Section determines which matches will be reversed in local play. It also states that a Section must determine one of two methods of DQ for championships:
1. Run the ratings after the conclusion of a tournament, and let the matches of a DQ'ed player stand (but he is not allowed to advance to Nationals).
2. The ratings are run after the tournament and the last match of the DQ'ed player is reversed to 0-6, 0-6.
In both cases, it would seem to indicate that the team you described will advance beyond the state tournament despite the player's dynamic disqualification, but that they will obviously be without him at the next level of playoffs. However, it also depends on whether the Section handles the state playoff as a "championship" or an extension of local league play.
By the way, I had a friend that was on a team that won their state playoff 3-2. The matches were tied at 2-2, and their #1 singles player won 13-11 in the third set tiebreaker after saving 4 match points. The team celebrated, everybody got the trophies for winning, and they started making plans for Sectionals. However, one week later, they were notified that their singles player had gotten his third strike in that final match, and that their entire team win had been reversed! That was very hard to take, especially when the two singles players were obviously so competitively matched.