That is possible and something Bloom has tried before.
I've mentioned various cndidates who not only have undesirable contracts, but also actually fill vacancies on the Sox roster (Kiermaier, Inciarte, Lorenzo Cain, Rougned Odor). And there are probably a few pitchers who could be on that list as well (Danny Duffy, Alex Cobb, Johnny Cueto) and maybe some who are marginal fits for the Sox (Dexter Fowler, Jason Heyward, Justin Upton, Mike Moustakas, Nick Castellanos, Charlie Blackmon).
And then there are other undesirable contracts we have avoided mentioning, but might be in play. Some fill vacancies on the Sox roster (Robinson Cano, Scott Kingery, Jeurys Familia) and some do not (Chris Davis, Ian Desmond, Elvis Andrus) but could be accommodated. Maybe. Does not mean they should be. I'd be OK with Andrus (2 yr /$28.5 mill) at 2B, and Desmond's deal (1 yr/$10mill ) actually is not so bad that either team could easily part with the right pitcher to make the contracts amenable. But Chris Davis and his 2 yrs $46mill? Pass. The O's don't have a pitcher to trade that makes me think taking that on is a good idea.
Which deals might be worth taking on to get a pitcher?
Right of the bat, I like Cain, Kiermaier and Inciarte. In the right deal, I could get behind Odor, Moustaks, Castellanos, Andrus, Desmond, Kingery, Familia... basically anyone but Cano, Cueto, Heyward, Davis and Charlie Blackmon (.987 home/.747 road) . Also, the unmentioned Nolan Arenado, whose deal (6yrs/$199mill left)and home road splits (.985/.793) could make for one of the worst acquisitions of all time. And I'm split on Upton, so that one will depend on the pitcher. (Hint: Pass. The Angels are buying pitching, not selling.)
And there are probably lots more. Maybe the Sox can just go get Zack Greinke? (OK that would feel counterproductive after just dealing David Price.)
So there are opportunities if Bloom can find other GMs in a financial bind and feels like being the one guy spending money...