Is it possible for a Plastic Surgeon to remove a (breast cyst) during a breast reduction?

Yes, generally speaking, benign lesions such as cysts or fibroadenomas can be removed at the time of elective breast surgery.  It will be important that the lesion be definitively shown to be benign prior to proceeding;  it will also be important that the lesion be palpable, so that your surgeon is able to locate it during surgery. Best wishes for an outcome that you will be very pleased with.

It may be possible to remove a breast cyst during breast reduction surgery. You will need to have the appropriate diagnostic tests prior to the surgery and discuss your options with your board ceritfied plastic surgeon.  

Breast cysts can be removed during surgery, but finding them is not as easy as it sounds.  Cysts generally do NOT require surgery, but a simple aspiration procedure that a breast surgeon or radiologist can do without surgery at all.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search.