So long as your key is authorized for three sessions you should have no problem doing that.
You can check over at:
Home Page - Buddy Auth Portal
The site will give you all keys for any products you have licensed that are associated with thebuddyforum and also tell you how many sessions are active or can be active.
It can also be used to disconnect sessions.
For instance if you get DC'd and the buddy you're using says you have too many sessions just log in there and disconnect it and you should be able to log right back in again.