No, won't hurt a thing, ust be sure the outlet you plug it into is grounded or the surge protector won't work. Magnetic coil ballasts are pretty durable. Never used a surge protector, never lost a bulb, and never had a problem. Not so sure about digital ballasts, I hear they're more finicky.
My ballast is digital and I am running it on a surge protector with no issues. I have ran magnetic ballasts before also. The only difference I have noticed is that the digital ballasts seem to be more efficient on electricity and they don't get as hot as the magnetic ones.