I wouldn't know about free hosts but even shared hosts like hostgator have quite high limits. I think the real trouble represents the number of concurrent forum users trying to do stuff at the same time. For example my forum has over 4000 registered users but I've never had more than 30 online at the same time so that was no problem at all.
Cogito ergo sum! - I think, therefore I am!
- Rene Descartes