sure can! You'll need to get something called waste canvas. When you're done with the project, dampen it and gently pull out the canvas threads. I've not bought it in a long time but I bet Michaels has it.
but I've done lots of waste canvas work on sweatshirts. Turns out great. I find a spray bottle and tweezers or needle noze pliers are great for pulling out the threads when I'm done.
This method also works great for cross-stitching on alternate fabrics for pillows or wall hangings.