If I have to take a crack at it, here's my guesses as it goes for basketball and football.
1. In women's basketball, I think that as long as Geno Auriemma is the head coach there, the Huskies will be fine. UConn should still be a Top 10 program regardless. But depending on whether recruiting at other AAC schools are like, will the team start playing with less intensity once conference play starts? Then after Auriemma leaves or retires, if the rest of the AAC isn't improving in women's basketball, we could see the Huskies decline like Louisiana Tech and Old Dominion have because they are not in power conferences.
2. In men's basketball, we have to keep in mind that the Huskies have won more championships than all schools except for Duke, Indiana, North Carolina, Kentucky, and UCLA. On top of that, former head coach Jim Calhoun has won all three of the Huskies' national titles, in 1999, 2004, and 2011 so the thought of UConn as a top men's basketball program is still fresh in our minds relatively speaking. And it's not like the conference name "AAC" is going to override the UConn brand, which has very strong cache in men's college basketball. And that's what current head coach Kevin Ollie will focus on since there will be plenty of great non-conference matchups the Huskies could get into as well. Here's a take on how UConn in the AAC may not be such a bad thing. But like women's basketball, it may not be surprising to see the men's team gradually decline too in a worst case scenario.
3. For football, this has to be a blow. As late as 1999, the Huskies played in what is now Division I FCS Football in the Atlantic 10 Conference, where they played schools like New Hampshire, Richmond, William and Mary, Delaware, James Madison, and Villanova, all programs that still play together in what's now the CAA football conference as the A-10 doesn't have football anymore. They ultimately got into the Big East where they were competitive and got to play in the Fiesta Bowl in 2011 after winning the conference. Now, the AAC football conference appears to be a mid-major FBS league, something that I don't think that UConn wants to be considered to be.
And lastly, I still think that UConn could end up in the ACC sooner or later. The ACC I think provides a great geographical and academic fit. But also, the ACC's basketball rich tradition fits right in with UConn's core competencies athletically. But at least one institution that still could prevent Connecticut from getting in the ACC is Boston College. In the past, BC has had desires to be the flagship college team in New England and felt ACC membership would do that. But bad blood from a lawsuit last decade doesn't appear to be an issue in that at all.
So those are my thoughts as an outside observer on the issue. But what are your thoughts on how UConn will be in the AAC, not just this season, but long term? Sound off in the comments below.