Is there a way that the rioreceiver can "wake up" a computer?

Yes. When you hit the power switch (to resume, not from hard power off), the Receiver will broadcast the necessary magic to wake up the PC that it originally got its firmware from.

Assuming you've got a network card and BIOS that support Wake-on-LAN (for that is what it's called), then it ought to wake up your PC (assuming you turned on that setting in the BIOS).

You say in your other post that you don't, however.