You can but I’d try this first. Get a good sized chunk of material and use some transfer scraps. Figure out the best time to use for the least amount of heat. Putting a chunk of drywall behind the transfer spot helps to pull heat through the transfer and cloth and will save you damaging the sponge underneath. This is important because the felt should be stretched and installed first. If you don’t apply the transfer after installation it will rip/skew/pull when you tighten and install the felt/cloth.
Thought about making a design for my black speed cloth I put on my Barrington table. I'll be using Siser Easyweed heat transfer vinyl. It's made for Cotton, Poly, and blends.