Not if filled and painted over., which is the only disadvantage I see aside from a possible wood mismatch.
An odd thing I was thinking about since reading this thread was Kurt Cobain's strat that he destroyed in the studio during the Nevermind sessions was a tremolo Stratocaster that had a TOM and stoptail installed, the TOM was installed where the pivot screws attach (not sure how good the intonation was though), and the stoptail was installed behind the rout. Not pretty but it seems that it worked well enough up until Endless Nameless.
It can be done, but a more attractive solution is to use a hardtail, even then, there's sill some fill work for it to look clean as most are string-through and have 3-5 screws holding the bridgeplate down. It'll be a lot easier to fill cleanly than the above blocking method.