When using "Fast User Switching," does everything still run when I'm on the other account?

Everything will continue to run in the background. (I just tested it.)

If you use a processor/RAM intensive app under another account, the account running the video conversion may slow down considerably. If the data stream is interrupted, errors could occur.

BTW, some apps, like Adium, are Switching aware. You can have it set your status to Away or Offline when switched.

Things should stay running fine, but your video convertion might encounter errors if the second person uses a program which takes lots of memory, or is forced to reboot or crashes.