I see no reason why this couldn't be done. I would guess someone has already done it. Just plain serial communication really. Your PIC is just a screenless terminal.

In fact, if you have the getty activated on the PC serial port (login prompt,) you could conceivably have the PIC enter in the username and password for the console automatically and do things entirely in the background. You just need to conform to the telnet protocol and either turn echos off or understand everything that will come from the PC serial port. (Like send a <CR> and expect to see " Login: " )

It could also be done in Windows or MacOSX. With additional free add-ons, you can make windows commands to do just about anything Linux can do. Like:
Find running processes and kill them.
Start new processes,
etc, etc.

Good luck,

Chris