I'd personally say "no," for a few reasons. The first, if you take the idea that it is a different binding domain, and try to see if it could fit with principal B, then "John(i) wanted to buy him(i) a new pair of shoes" would be possible, but it isn't.
The "want" in here is a "control verb" - a verb that has the same actor for both the matrix and subordinate clause, and so if you take that analysis, there is an implied (or moved) John also in the subordinate clause.
Also compare with "John(i) wants Joe(j) to buy him(i) a pair of shoes" vs. "John(i) wants Joe(j) to buy himself(j) a pair of shoes" - with an explicit agent different from the matrix clause's.