Accidentally deleted steam download files

It depends on the game, but essentially anything can happen - the game might run normally, the game might not launch at all, or the game might crash unexpectedly. It's not really worth finding out, so your best bet is to have Steam verify that all the game's files are present and accounted for.

What you should do is right-click on the game in your Steam library, then go Properties -> Local Files -> Verify Integrity of Game Cache.

This will make Steam double check that all of the files it expects to be present are there, and it'll download stuff if anything is missing. Once it's done, the game is definitely ok to play.