Yes, a no till drill can work good on established sod as far as putting the seed in contact with dirt. We use those in these parts too. Most wheat is planted here with a no till drill direct seeded into soybean stubble or after a pass with a vertical tillage harrow. Bermuda sod drilled in the fall is going dormant. Probably dormant later and greens up earlier in Texas than NC though. Fescue is a cool season grass. Bermuda is warm season. Bermuda spreads from the rhizomes when it resumes growth in the spring. Almost impossible to do any damage to bermuda with a no till drill disk in the fall. Fescue does not spread by rhizomes. Might be some risk to a fescue stand running a no till drill through it. Pasture here is sometimes a little rough, irregular shaped, maybe steep slope and may not be easy to drag a no till drill over. We do tend to have some mud through the winter. Us small timers here may not have easy access to a no till drill. Broadcasting clover seed will give a pretty consistent but not ideal seed depth. No till drill on rough ground will have some seed too deep and some not covered and some just right.
Wish I had clover, but don't know how to maintain clover and still use broadleaf herbicides on my weeds. Do you clover guys not have weeds?