They DO cross-check logs, and if you worked a few stations in the contest, most contests will be very glad if you submit your log. If you do like me--just play in the contest for some fun, no intent to compete--you can submit what's called a "check log," one that's just for checking other logs. It never hurts to submit a check log; most of the time the contest organizers are glad to have it!
If you only worked one or two stations in the contest, the people who worked you might lose points--the contest doesn't know you're for real if only one or two people claim the contact with you, because it might be a miscopied call. All the more reason to send in your log.
By the way, GOOD for you for giving contesting a try! Contests can be a lot of fun, even for non-contesters like me. :-) I got one all-time new country this afternoon--that's ALWAYS fun! :-) And contests are a great way to work a lot of DX very quickly, which is great, and a lot of contesters use LOTW, which is also great, and contests tend to bring lots of activity from places that aren't always easy to work--which is ALSO great.