Hi 3rhobbyshop, welcome to Scrapbook.com. Hope you can find some inspiration here and share some of yours.
Sadly, I have not looked at a cricut cake so can not say for sure how it would work. I can not for the life of me think of a reason that it would not cut vinyl. Especially if there is no residue from the fondant in the machine. It might be worth a try....assuming you have everything but maybe the vinyl, it would not cost that much to try out a sheet of vinyl to see what would happen.
I use some of the cake designs to cut with paper... surly it would work with vinyl on a cake machine!!
I was just watching YouTube and see where they cut paper with a cricut cake using the paper cutting mat, which you would probably do if using vinyl. I also saw where they used the explore to cut fondant... that would lead me to believe you can use the machines either way. Obviously you would not use the regular mats for food products or eat anything that came from a machine that is not food safe.
I would give it a go!! If the only mat you have on hand is a new cake cutting mat I would try that with the vinyl as long as the mat has a sticky coating like paper cutting mats.
Here is a link to cutting vinyl with cricut cake.......I did not watch it but it is there.