Apple - Can I add a custom ringtone to my iPhone without syncing to iTunes?

Unlikely.

Such functionality is indirectly excluded by the iOS Developer Program Licence Agreement under section 3.3.4.

There it is stated that applications may only write data to an application's designated container area on the device. Therefore, the library data for ringtones cannot cannot be manipulted unless there were API to do this.

I am not sure if I'm allowed to post a direct link here, therefore use this google search to get to the document.