Deirdre almost certainly did not survive, however her death is never explicitly stated, so there's always that slight possibility if you want to cling to it. She never shows up again in the series except as a pattern ghost. Her relationship with Corwin is almost that of fraternal twins. They have the same mother (I'm not sure who's older) and have always been very close. Personality wise Deirdre is like a female Corwin, but not as battle-hardened since the princesses of Amber didn't seem to have the same constant feuding (even as children) as the princes. I believe her colors are also very similar if not exactly the same as Corwin's silver and black.