I don\'t think it\'s possible for $network not to be filled...it is standard protocol to send a network name to a connecting client in raw 005, and I can\'t think of any reason for an IRCd not to follow this practice.
The maximum number of channels a person is allowed to simultaneously be in are also included in raw 005. At least, that information is sent on UnrealIRCd, and while I haven\'t tested it on others I would be that they would send it as well.
After connecting to DALnet, for instance, you receive a message like this, displayed before the MOTD:
<- :aeon.ix.us.dal.net 005 YOURNICK NETWORK=DALnet SAFELIST MAXBANS=200 MAXCHANNELS=20 CHANNELLEN=32 KICKLEN=307 NICKLEN=30 TOPICLEN=307 MODES=6 CHANTYPES=# CHANLIMIT=#:20 PREFIX=(ov)@+ STATUSMSG=@+ :are available on this server
And it says in this message that the maximum number of channels you are allowed to be in at one time is 20 (MAXCHANNELS=20)