Effect of changing timeouts to 3 hours

The growth would depend on the number of clients connecting, and what kind of persistence is used. It's not just a matter of number of clients, as many clients could share the criterion for persistence (e.g. IP-address).

I would start by looking at the size of your current persistence table. However, before that you may want to determine whether it even makes sense to extend it to such a long time, especially if the persistence would exceed the session timeout on the servers. In that case I'd question whether anything can be gained.