I wouldn't. The vaccuum may be hard enough that it will actually push the mat into the top of the foamcore, essentially denting the part of the photo/print that is going under the mat. Also, the mat will provide a small barrier and the vaccuum mount probably won't be able to press down on the center of your print properly, potentially leaving bubbles in the print. I'd drymount your picture first, then add the mat to the top of it.
You're still welcome to come by my shop and see how we do it some time.
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