Having seen how dust accumulates on a de-staticized LP even with a dust cover on, I would never play a record with the dust cover off. I have a HEPA air filter in the room with the turntable, and I don’t think that completely eliminates accumulation of dust--I think it comes off clothing I wear and from the HVAC system if it is on while playing a record.
I suspect that any difference in sound quality would be negated (for me) by any additional tick noises that added dust would cause, possibly permanently. The three turntables I’ve used in the last 50 years all had dust covers that could be placed down while playing records. My turntable is a SOTA Star Sapphire, and I suspect the vacuum holddown reduces vinyl resonances so that the dust cover wouldn’t make much of an audible difference, but I’ll admit I haven’t even made the comparison. I will, just out of curiosity, with some record that I don’t care much about.