I'm not totally against the idea, but my experience with purple heart wasn't great. It is one of those woods (my list includes paduak, purpleheart, wenge, and cumaru) that is very hard, very stiff, and NOT very elastic. One of those woods that will never take set, but will crack or fret readily.
I remember seeing exactly TWO adult-sized, decent draw weight, purpleheart bows, one backed with hickory and one backed with bamboo. They looked cool as heck, though.
I did make a couple really nice 45-48" kids bows with it, with bamboo backs which were really snappy little bows, but both eventually broke under essentially normal use by kids, taking big frets off the fades and collapsing.