Would pushups helo strenthen my shoulder muscles around the rotator cuff?

Suggestion. Assuming that you suffer from anterior dislocations, where the humeral head moves out the front of the socket, i would recommend you look at the thrower's 10 program. Concentrate on the exercises for shoulder... If you are doing to do push-ups avoid going deeper than 90 degrees at the elbow since this will put your shoulder in a vulnerable position for dislocation. Avoid tricep dips for sure!