This is a great question, and pretty common as who wouldn't want to breathe some LED life into their old style halogen driving lights that have served them well for so long.
Unfortunately however the only feedback we've ever had on people fitting the headlight conversions to driving lights is negative. You're welcome to try, but the reflector design is often not conducive to LED Headlight Upgrades.
That being said, the best option for LED driving lights, is of course upgrading to a purpose built LED light. We have a few options that don't cost much more than the LED globes, and at 1760 lumens each globe (3520 for a pair) a similarly priced bar or a bit more expensive set of driving lights would be much brighter and with a better beam!
For example, the Type-X Sport 8.5" are about 3 times the cost of the globes, but offer nearly 7 times the brightness - and have a guaranteed perfect beam pattern (and a 5 year warranty as opposed to 2 year on the globes)
Another closer example would be the ST4K 12" bar, 4800 lumens and only $20 more than the globes would cost. Also has a 5 year warranty and better beam pattern than the globes would give in the old driving lights.
All this to say, dollars for lumens you're better off buying a dedicated LED bar or driving light, and you're better off with a dedicated LED driving light from a performance perspective as well.
That being said, we understand people's desire to put higher performing LED globes into a vintage light, especially one that has some history on your vehicle. If that's your situation, our suggestion would be to hold off trying to fit LED headlight globes to a driving light and wait until you're ready to upgrade to a dedicated LED setup.