My wife had a week long business trip in St. Louis earlier this year and she FORCED me to tag along. I figured it wouldnt be all bad if i took the Wii for some GE action though. I was sadly mistaken. My wii refused to pass a connection test with the piss poor hotel WIFI, so Tito turned me onto using Connectify, a program which turns your laptop into a hotspot. I was able to play this way, but the lag made it nearly unplayable.
Depends on a number of things. Hotel wireless setup, room location, number of people staying that night, etc...
I've had playable experiences in some hotels, while not even being able to connect in others. Usually the A/V settings cannot be altered unless you enter 'maintenance mode' on the TV which can be dicey. Couple times it was just too damn dark to play and brightness could not be adjusted.
If you have a LAN adapter you can usually get an ether net cable from the front desk.