I’ve played records as long as most any one here and I don’t believe the warpage is the reason Not to store horizontal. I believe @billzame may be right about the bottom records becoming damaged. I’ve sorted through and bought many records that were stored horizontal. The problem with almost every one of them is ring wear on the cover. The ring wear got progressively worse the further down the pile that I went. IF the album had any warp, it was very slight and not problematic.
So 20 albums may not be a problem. Its not the best but if it is all you have, then maybe try it. But an alternative is a closet. I have some of my less desirable in a closet. My son once commented that there were albums behind every door