Yes, it is fine to take the check and not do anything to the car.
Some anecdotes:
Grandpa-in-law had an Oldsmobile that had significant cosmetic hail damage. He took the check, and renamed the car "Dimples".
We had a truck that was backed into in a parking lot. Took it to 3 places the insurance company told us to (same insurance company for us and the at fault driver) and they gave us the average of the 3 estimates. We pocketed the check, and took the truck to our friend who did work on the side. Made $1,200 on the deal (insurance gave us $1,800, guy charged us $400, we gave him $600). That truck was worth about $3,500 according to the insurance company; we could have had it totaled if we wanted to but instead just had it fixed (not a rebuilt title or anything--title was still clean).
My wife got in an accident with her car. Cosmetically, it needed a new bumper, hood, headlight, and maybe some work on the front fender. Underneath, everything was broken--radiator support, headlight support, windshield washer fluid resevoir, etc. We had been driving the car for a month before we finally took it in to get fixed. The car was worth about $3,500 in my estimation. The cost to fix it was $3,300. Insurance valued the car at $4,500. The shop, with the blessing of the insurance company and us, found more stuff that needed to be fixed from the accident (stuff that would have been fine and they were trying to keep our cost down since we didn't initially involve insurance). This let them total the car and we got the check. We had the option to buy the car back for $2000, but it didn't make sense to us when we worked it out with everything--but we were close to doing it.