Is there a downside to using Lens Correction to fix Lens Distortion?

It really depends on the lens and what is in the image, the subject matter.

Depending on the camera system you are using, the editing program you are using and whether the camera + lens manufacturer has built in any Auto lens correction you may or may not be able to turn all lens correction off.

Only you can tell if correcting lens distortion helps or detracts from the image quality.

Any time that pixels are moved and redrawn there is a small theoretical loss in quality. Most people consider it a necessary and acceptable price, just as any editing has a cost (rounding-off errors, etc.), but if the image has only naturally curved lines, as opposed to architectural straight lines, I usually do not apply a correction profile.