Is it OK to play CDs on my cheap DVD player?

That depends on what you mean by OK. Can you do it? Of course. Will it sound any good? Definitely not.

“But Mike, I’ve heard all CD players and DVD players sound the same?”

That’s like saying all wine tastes the same or all guitars sound the same. To a child or someone with limited experience, they do. They really don’t, but knowing and understanding this comes down to experience.

If you’ve never heard a really good CD player in a really good system, you’ll think CDs sound ‘fine’ played back on a cheap DVD player, and you’ll think that means the same. But, in a high-resolution system, the difference between a good dedicated CD player and a cheap DVD player really is night and day.