Cera, I'm sure they would have to say for sure themselves, but if it's an LP then they would probably want the associated cover... Something extremely rare might be an exception, but that tends to be important. With singles/45s, they may be more flexible... 45s tended to be sold in more generic covers, anyway, so it wouldn't be as important. Hopefully they will check this occasionally and answer for themselves, but you may have better luck calling.
We do not buy LPs without covers
The used records I bought all had a cover. I never saw any there that did not.
Thanks! Your answer is awaiting moderation.