Depends on the camera, adapter, and lens, but in my experience, if you are using a good simple ring adapter (no optical element) that holds the lens the correct distance away from the sensor, no. There is no image quality hit.
Canon 5DMkII + adapated Contax/Yashica Zeiss Planar T* 100/2.
Panasonic DMC-G3 (mft camera) + OM-mount Olympus Zuiko 50mm f/1.2 on a tilt adapter.
OTOH, I'm not a pixel-peeper. And Roger Cicala of lensrentals has emperical proof that adapters can cause image quality issues (although, read his article carefully. They deliberately plotted the data in a way to make the problem more self-evident (to make it really obvious if they need to service a lens), so everything looks a lot worse than it is in reality). And, as he says at the end of the article:
What Does It Mean in the Real World?
Like a lot of laboratory testing,
probably not a lot. Adapters couldn’t all stink or people wouldn’t use
them. Like a lot of tests, you can detect a very real difference in
the lab that doesn’t make much difference at all in the real world.