Will my knocked-out tooth survive if it's put back in right away?

It's possible. The main determining factor is the developmental stage of the apex or the end of the root. If you are older and the tooth is fully formed then most likely the tooth nerve will die but most of the time the tooth will remain in place, it may need a root canal though. Sometimes the tooth will heal however.
Survive? What is ment by suvive? If you mean will the tooth stay in your mouth then the answer is most likely with the proper treatment. If you mean the nerve still alive in the tooth then no. It is important to see a dentist right away.