Adjust Covers To Force Baseline?

Does Adjust Covers change JEPG progressive to baseline?

If not: How about if I go from JPG to PNG an then from PNG to JPG?

Yes, this is the recommended way. But as png is also a valid picture format, you could leave it like that and avvoid the additional loss of quality by the 2-step-transformation in lossy formats.

Make sense since I can always do the conversion to jpg if I have a problem