I've never heard of "full overlay cabinets". Full overlay *doors*,
yes; cabinets, no. Full overlay doors are "full overlay" because they
are on the outside of the face frame instead of being recessed either
fully or partially. There is normally a reveal with full overlay
doors - an inch at least and that inch would accommodate a molding.
Your box cabinets won't, good luck in hanging them.

Well , that's what I meant, full overlay doors. Kraftsmaid cabinetry
sells 3 versions of overlay:
Full overlay
1" overlay ( meaning 1/2" of the cabinet frame is exposed)
1/2" overlay ( meaning 1" of the cabinet frame is exposed)

To accomodate a molding for full overay doors, there is a piece that
goes on top of the cabinet, like a bullnose, which extends past the
frame and the door so you can put the crown on this "bullnose" piece.