I wonder if he would have publicly supported Adams had he lived, so that he would have been re-elected in 1800. But then again, Hamilton was against Adams at this point, so Washington might have been also.
Washington and Hamilton were very personally close but I don't think Washington would have started following Hamilton's lead on matters like this rather than the other way around, at least not at this point in Hamilton's life (his circa-1800 political ideology and approach were extreme even for the Federalists--more like a Bonapartist or a Frederick the Great simp than like Adams even at his most "muh national security"-minded).
Hamilton literally tried to oust Adams in 1800 and replace him with Pickney (of course, his plan backfired, expediting Hamilton's political fall - and the fall of the Federalist Party's fortunes in general).