No. User levels are stored globally. How you use them, however, is up to you. Just because the level is globally stored doesn't mean you have to use it that way-- you can check $network or $cid in your events to verify that the user in question is on the right network, thereby implementing network specific user levels. Of course, you cant share user level numbers/names, so you do need a unique one for each network, but that should only be a minor issue.
