Can a person work out at the gym and do straining exercises after a leg bypass operation?

Yes. Depends on type of surgery. One healed u should be able to do it. Consult with surgeon who did your surgery.
Absolutely. The purpose of increasing leg blood flow ( balloon streaching with or with stent or bypass ) is to keep both leg / foot length as well as function. Exercise is an important part of recovery after surgery. It is also part of preventing further problems. Don't forget - stop smoking, normalize cholesterol & triglycerides, normalize weight, and exercise ). An abdominal support can prevent hernias.