Would it be ok to do this for my guinea pig?

It will be fine. I have a 2x6 C&C cage and buying bedding is way too expensive and messy so i use fleece and towels. In the "kitchen area" of their cage i have a litter box where their hay is and they poop a lot in it which makes the fleece easier to clean and it smells less, this way i only have to buy a little bit of bedding and not a lot.