Yes, you can. However, Furry Weekend Atlanta recommends that you do not do this. There are some issues with this that you should be aware of.
If you are going to pay in cash, be aware that the hotel has the right to, and most likely will, request a deposit when you check in to cover any incidental charges (telephone usage, room service, etc) made to the room over the course of your stay. This is a standard practice at most major hotel chains worldwide. This requested deposit could be quite large and may be up to and including two (2) nights at the room rate, but may be more or less.
If you wish to pay with cash, Furry Weekend Atlanta recommends that you use a credit card to secure the deposit on the room when you check in, and then pay the full balance in cash on checkout. That removes the need to pay the cash deposit before being allowed to check in.