I dont see why not, assuming the pic uses a decent serial routine,
and you connect via a max232 line driver for a guarantee, unreliable otherwise.

I dunno if I can just "throw" together even something that simple,
looking at my archives, I haven done any actual MP-Lab PIC coding since October 2003 !
Ive got the parts, but the skills may be a little weak. And Im on day-shift which limits my "play" time.

But I'll give it a try... Gimma a couple of days...