I think it WOULD be an issue, because swelling clays generally swell when wetted, then shrink when dried. There would be potential for cracking, loosening, etc. as a result. In a liner, you might be able to keep the clay approximately at the compaction moisture fairly well if there is a membrane liner over it, but you can't expect to keep the cap at constant moisture long term.
I'd avoid it.
Regards,
DRG