They can check your IP though.
So if it was only that IP addy on there, that wont work, I3romley.
On topic:
I think you're best to go with honestly.
If you're sorry, let them know.
Etc.
Good luck.
Also, on my friends main, it got banned for same reason, I appealed it for her I typed: " I made no offences, I've had this account for over five years, I get banned for a mistake of RL trading? Meanwhile I wasn't even doing so, someone was giving out free money, not sure why, I accepeted it, who wouldn't accept (whatever amount of money)?...I didn't know it's wrong to accept stuff from other players. I got banned? Because of that? Accepting stuff. Geez, so what, I'd get banned if I took a bronze sword aswell? In tut island, you give free stuff out, why can't other players? I don't see any difference, if you (Jagex) gives out free items at hoildays, tut island, random events, what's difference if pixels do same? " Few days went by, they unbanned her account, she was crying of happiness, because she had that account for a while and Runescape is only thing she can look up too, she said she'd give me RSGP, but I told her " You're my friend, I like to make my friends happy, I don't want your gold. "