To some extent (e.g. American retains the -r dropped later in England) but really once two dialects begin to diverge they are both equally likely to innovate. And New England is as likely to innovate as anywhere else in America (good example is the Boston variety that drops -r, apparently an imitation of British English). What you might find is that New England had more regional diversity, compared to the recently-settled West. (Just as England has more diversity than America as a whole, having had more time for evolution to occur.)

I don't off-hand know of a single UK vs US spelling difference that actually reflects a pronunciation difference. All Webster's reforms were fairly trivial. Any takers?