Hi I am sure you can as long as you have a thick layer of batting or towels underneath to help absorb the urine. Perhaps you could also try flannel or something like that, it's basically a big cushion to keep the guinea pigs dry and not walking all over their urine.
Hope that helps
The difference is that fleece wicks moisture away -- rather than soaking up fluid, it makes it run through to the layers underneath. Therefore, fleece stays dry on top. Other fabric won't. With another fabric you'll probably have to change it every day but if you're up for the work, it's a possibility. Otherwise I'd go with a safe alternative bedding (kiln-dried pine, aspen, paper pellets, etc.).
I use the aspen bedding with a layer of Carefresh on top, which works quite well. Granted, the Carefresh can get expensive, but I (and my Doodles) likes this system since I can pat it down. It works out well.
I use fleece and also flannel with layers underneath. My daughter for christmas gave me a small hand held vac. I love it and seems to make it so much easier to clean their pen. However they scatter when I turn it on. I'm thinking on re-designing their pen so I can easily get around their pen when I clean.