Olivers and Whites pull start just fine in Over and Direct (unless the clutch plates are gone).
If you're planning to pull the engine to rebuild the clutch, there is no better time to fix the O/U, you're right. Do a couple of things first though. Get a pressure gage that reads to 300psi, and check your clutch pressures (over and direct). I'll have to look at my service manual, but a 2150 over/under should produce something in the 160psi when engaged. As long as you are building that much pressure, then your pump and piston seals are still good.
I hate doing things twice, so when I rebuild these I buy the seal kit and replace them all. However if you're on a tight budget and the pressure test above meets spec, you can get away with replacing the sprag clutch (that is why your under drive does not work), and your fiber overdrive clutch plates (unless the metal separator plates are burnt as well. Of course check your direct drive plates too while in there. Also, don't cheat this, replace your input and output shaft seals. These cost very little, but if you put this back together and the old seals leak, you will be very angry.
If your sprag clutch has completely failed and you have material transfer from the sprag onto the output shaft, people will tell you that your output shaft is ruined and that you need to spend a few thousand $'s on a replacement. That's not necessarily good information. If that's happened, chuck the output shaft into a lathe and run it while using fine grade emory cloth on the area where the sprag clutch rides. As long as the area cleans up and it still within spec (these numbers are in the service manual), the output shaft is perfectly fine. These output shafts are ridiculously hard, and the sprag is soft. People panic when they see material transfer and make bad decisions for no good reason.
The overdrive clutch plates are the same as those used in a C4 Ford automatic transmission, they are available for about $5 each, so don't overpay. I've not yet found a replacement for the direct drive clutch plates, but they're only about $20-$25 each, so they're not terrible.
The first 1 of these I rebuilt (White 2-180 with heavy duty over/under), I purchased everything new from Agco, and the parts costs was about $2k (sprag, plates, seal kits, bearings, etc.). Since then, I've tried a little harder and found that if you test first and figure out if the piston seals are still good, and then only buy what you need, the rebuild costs for these things come WAY down. Sprag will cost you $300-$400, there is no alternative to this. The sprag is installed 1 way only, so don't screw that up, it's spelled out correctly in the manual.
These over/under's are very repairable, and they do cost money to repair, but all parts are available, and they are not nearly as scary as some would make them out to be. I'm happy to help you along the way on this repair as best I can.