Is it possible for a manned flight to rendezvous with Mars, do a couple of orbits and return to earth before it gets to far away.?

Interesting idea, calculations have been made for various Mars missions but a flyby would hardly justify the cost. Comparing it to Apollo 8, the Moon mission was of relatively short duration and considerably less expensive. Most likely the first human visitors to Mars will have a lengthy stay with numerous objectives. The prolonged stays in the ISS are a dress rehearsal for future Mars missions.

If you Google "Mars mission trajectory", there are quite a few research papers discussing various Mars mission trajectories.

One example:

https://engineering.purdue.edu/people/james.m.long...