The new stadium isn't a necessity, but proximity to Boston may actually hurt the PawSox in terms of trying to build AAA revenue. The new owners of the PawSox may want to increase seat licenses, luxury box type stuff, but all of that money may prefer slightly less amenities and higher cost to just go to Fenway. Hartford would probably be able to support more of that kind of thing, although it's kind of a "believe it when I see it" deal. It should be noted looking at all of those AAA revenue lists that the teams that do best are far from MLB options.
Sacramento - 2 hours from SF and Oakland.
Lehigh Valley - 1.5 hours from the Phillies (Philadelphia is huge, you can get to the northern outskirts in about an hour, but it's another half hour to get to the stadium, more with traffic)
Round Rock - 2.5 hours from DFW, 3 hours from Houston.
Memphis - 4 hours from St. Louis, 5 from Atlanta
Columbus - 2 hours from Cleveland, 2.5 hours from Pittsburgh
etc. etc.
As far as I can tell the PawSox are the only AAA team within an hour of MLB. That said, given the skyrocketing price of attending a game in Boston, you would think they could do something similar to what the IronPigs are doing, and Providence has about twice as much population to draw from as Allentown. (By SMSA). Perhaps the idea will be to move first, but I hate the idea of another shitty for taxpayers boondoggle stadium, and I would think they could at least try to expand their appeal first. While the PawSox do poorly by revenue, they do very well by attendance. The question is what they can do to expand revenue without negatively affecting attendance too much. It seems there is an opportunity to be a little less family friendly (super cheap ticket blocks, free parking, etc. are not as easily found at other AAA venues).
On the other hand, while what might make the most sense is for Pawtucket to get a AA team, the SeaDogs aren't going anywhere, so it would probably have to happen with another franchise, which then means you need to attract those owners, etc.