I doubt it. It's very, extremely I'd say, unlikely that we can get more value for Allen than what he brings to the team. I don't see financial restraints having any kind of impact, because Ray Allen is an expiring contract. To save $2M or something like that? Not happening, if we really need to save that, we're doing it in the free-agents signings. I'm not opposed to move Ray Allen (or anyone else), I just don't see an offer worth to think about being made.
And of course there are budgetary restrictions: I agree with the corpus of Nick's reasoning, I've made a similar one in a thread about Glen Davis. Ainge probably will only have $5-$6 millions to spend and an entire bench to build.