You can of course downtune like that, but E down to C will generally sound pants IMO, any low frequesncy will probably just choke out through sloppy action, you won't gain anything over simply playing a standard octave C on the E string (8th fret), that generally sounds pretty fatter compared to a C on the A string (3rd fret).
Again, considering it's for one song, I'd just get an Octave pedal, which is easily implemented into other songs too.
Si