I am not an advanced user but been using Ubuntu since 2005
You can actually do and at the same time you cant,
Scenario 1 - Getting live just ONCE
When you get Live through your usb stick, just get a wired cable, and install the wireless drivers. Once you are done with it, surf internet using your wireless NIC card. Okay i know that sounds lame.
Scenario 2 - Getting live again and again
Get your ubuntu iso image burned on a cd or dvd (whatever suits you). Get live, and install ubuntu on the usb disk.
Now whenever you plug the usb, you ll find that ubuntu is actually installed over it (saving + dynamic storage). Get a wired connection for a while and install the drivers once. And enjoy using wireless every time you boot from usb.
Note: I dont know, may be there are ways to tweak the image. However i consider scenario2 the most safer one.