I have seen lots of giclees around, and some are 'hand-embellished'. So painting over them is common but I think it's usually in acrylics. I wouldn't trust them for oils - they're not primed and the oil could easily sink in and rot (or not sink in and peel off). If you have a printer that uses archival inks, and there aren't many, you could print directly on something like Fredrix canvas made for printers and then you'd know it's a primed surface.
I don't make reproductions of my work personally, so can't tell from firsthand experience.

Sorry.