Lost or stolen ipod: can the finder turn off Mobileme?

Question

I've searched the forums and can't find the answer; lots of lost ipod threads out there so maybe I've just overlooked it, though.  Apologies if so!  I don't have an ipod myself to fiddle with to find the answers.
My daughter lost her ipod touch, 4th generation yesterday afternoon (or possibly it was stolen?).  She did not have a security code required at the time it was lost.  She had the "Find my ipod" app installed, but it was two hours before she was able to get home to go on-line and a) add a message and b) add a security code.  We're assuming that at this point, if anyone tries to turn it on they'll get the message she posted with her phone number and they'll be locked out of using it since they won't have the security code, and hopefully we'll get some information as to its whereabouts.
However, what happens if the finder (or thief...?) turned it on during that two hour period before she had logged onto Mobileme to add the message/security code?  Could they have gotten into the Find my Ipod app and disabled it or turned it off?
Also, we live in a rural area where lots of people don't have wireless at home yet (yes, some people still have dial-up!).  I know that the Find... app requires wireless.  I assume, then, that no security code will be required if someone uses the ipod out of range of wi-fi?  And if they do so, and if the answer to the first question is "yes", then presumably they can just make sure that they're out of range of Wi-fi and go in and disable the Find... app?  or can that only be disabled from the mobileme website?
Thanks for any info.

Answer 1

Thanks to everyone for your helpful information.  I really appreciate it!
Happy ending for my daughter:  someone turned her iPod into the school office this afternoon.
Strange ending for Mobileme, though, and not particularly confidence-inspiring:  even after the iPod was home and on-line, Mobileme continued to show "Location not available".  Mobileme is clearly finding it:  I just tested it by sending a message from Mobileme to the ipod, and it displayed immediately.  But it doesn't give any indication of a location.  I would have thought it might have at least displayed an IP address if nothing else, which would be helpful at least for telling whether it was at some known location (e.g. I can easily enough figure out what our IP address is at home, what the school's IP address is, and a few other locations like her cousin's house, grandparents' house, etc.  That wouldn't help much with a theft situation, but would surely help if it had been left somewhere.