Thanks Sarah for this research but I have the strong suspicion that the reason that you can't find anything is because she never existed under those names, and that we have two (or more) men named William Drake with a combined wife.
The Visitation of Norfolk, p. 197 (not always the best source but a good starting point), has Ann Marsham married to William Drake of Norwich
A chapter about the Drake family from Essex, by the esteemed late English genealogist Sir Anthony Wagner, in the book The Drake family of New Hampshire ... has a William Drake, married to Joan Merrylls; at the moment the William Drake Jr profile the son of William Drake Sr and Joan Ann Marsham is the one married to Joan Merrylls
I'm not sure where the second husband Thomas Everard fits into all this, and maybe finding him and his will that supposedly names all the children of William Drake and his wife Joan might be one avenue to follow.
Unfortunately tangles like this are still reasonably commonplace on WikiTree, particularly in the pre-1700/pre-1500 area and I don't have time to do more research, but I would definitely recommend that if the two Marsham profiles are merged that they are disconnected from the Essex Drake family and connected up to a William Drake of Norfolk profile, if that doesn't exist already.