I think OP has an interesting premise. But I think it is a difficult question to answer because there are a ton of variables to deal with.
First, since the new CBA was put in place we haven't had a tremendous amount of cap space. Second, most big name free agents choose to stay where they are because they can make more money there. Third, until Paul came we never really had an enticing star (sorry Toine fans) or a good team under the CBA. Fourth, we have high state taxes. Lastly, when basketball is played here the weather sucks .
Point is, maybe we have a chance at a tier 1 FA in 2012 because for once we have cap, a good name and an enticing star (unfortunately unless this global warming stuff kicks up the weather will still be terrible and Patrick will be Governor so taxes aren't going down). But even then, who says there will be any available FAs and even if there are who says they would prefer here to another destination.
Gotta build other ways in the NBA, very few places land top free agents!