As the cuttle kid dies are thinner than the regular ones I'd guess that no you can't. I've just been battling with using the kids ones in the regular cuttlebug. I'd bought some and then couldn't use them but have persevered and have now come up with a combination of chip board and cardboard pads that allows me to use them. It's too bad they can't be inter changed.
you can pretty much cut any die in the cuttlebug machine. apparently you can also use the brass stencils. check over on the cricut board because they have all kinds of info on how to cut everything. I've had no problems with my qk dies, sizzlets, and the few random regular sizzix dies, no problems with the cuttlekids either. maggie