adding the brown sugar before carbing it definitely won't leave a nasty taste. don't expect much of a brown sugar flavor anyway, it's highly fermentable and doesn't leave much flavor behind, kinda lightly sweet rum note IME.
you can use this calculator to see how much brown sugar and various different sugars it takes to prime:
out of curiosity, is 65F ambient or wort temp? if ambient, be aware the internal temp will be a few degrees warmer during active fermentation. in most ales its best to keep the wort temp <70, british strains get especially gross over this