I'd suggest asking around on one of the mobile forums for cell phone enthusiasts.
Yes, this will work - I've emailed myself ringtones.
It may or may not work, with different carriers and different phones.
Verizon tries to block this, (so that they can collect revenue from "ringtone partners") for example, but some specific phones allow it.
For a while, all new phones had it blocked, then they apparently started backing-off on policy.
You need to know about any tricks for a particular phone. For example, some phones want the file named "example.mid", (Midi) even though the content may be MP3.
There may be another mechanism used by these sites. If so, I know nothing about it.