I can't find any evidence for
RACHAEL in the bible. In the Hebrew bible it's RAKHEL, same in the Greek Translation, and
RAHEL in the Latin version. I don't know about older English translations or maybe French or maybe adaptions to literature.
But I assume the E slipped in, just because it looked fanciful and would still be pronounced the same way. Or as you say, to make it look like
MICHAEL or
YAEL. But here of course the EL part means something: "God", or in the case of
YAEL it's part of the vocabulary word.