In the short term, no.
In the long run - Yes.
Over the long term running without a thermostat won't let the engine get hot enough to get all of the moisture and volatile stuff out of the lube oil system. That degrades the oil quicker and lets acidic crud build up in the oil.The old engines didn't have that hot a thermostat, but they still need one if you're going to run it for a long time.