From what I've read, I think you're partially right;
Morgan (and the variants
Morgana and
Morgaine) have been in use for females - or rather, for one specific female literary character - since the earliest
Arthur stories were published in the 12th century
AD.
However, it seems very likely that the name
Morgan as used in the
Arthur legends is not the same
Morgan as the Welsh male name in the database. The bits and pieces I've read suggest that it may have been adapted from the name of a Welsh goddess (Modron), or even from the Irish
Morrigan (but that doesn't seem likely if you look at the characters of
Morrigan and
Morgan, they're certainly not the same character).
According to the best resource I know for mediaeval-era feminine names,
Morgan or variants weren't being used for girls when
Geoffrey of Monmouth wrote
Vita Merlini, the first major recording of the
Arthur legend; nor did
Morgan become popular for girls in the three centuries following.
http://www.s-gabriel.org/names/talan/reaney/
www.archaeochrisell.blogspot.com