Sure, except unlike Bile Cag didn't need help. Every power Cag has is something he made himself from scratch. He doesn't owe anybody anything.
IIRC, Cag's backstory is that as a kid he was dying of some incurable illness and said "fuck that shit, I'm way too smart to die" and invented an entirely new form of magic he called Alchemy so he could just build himself a new, better body that wasn't so fucking shitty.
That new body was female. He never bothers to explain why, exactly, but I guess when you are an archwizard at age 12 you can do whatever the fuck you want. And it clearly wasn't an accident, cause he's stayed female at least the last 3 bodies.