I'm going to see a plastic surgeon soon to remove a cyst. Is it also okay to get a breast implant?

Usually yes. Usually, it is possible to remove benign lesions and undergo breast augmentation surgery at the same time. This is especially true if the “cyst” is located in the vicinity of the incision planned for the breast augmentation procedure. Your plastic surgeon will be able to provide you with more precise advice. Best wishes.
Unrelated. The two things are really unrelated. Of course you can have breast implants, if you understand the procedure and have made an informed decision. The cyst has little bearing on that decision. If the cyst is infected however, you might want to decide to have them taken care of at different times. Good luck to you, dr. Fred.
Yes. As long as the cyst that is being excised is not in the location of where the breast implants are being placed it is absolutely fine to have a cyst removal at the same time. I would usually place the implants first have a sterile field and then excise the cyst.
May be fine. If the cyst is not an indication of underlying disease and is solitary and easily removed then I do not see that there is any contra-indication to proceeding with implants. However, if there are multiple cysts, then proceeding with implants may not be a good option as multiple follow up biopsies or mammograms may be required.
You Certainly Ask. Removal of a breast cyst and breast augmentation are separate procedures and require independent evaluation and consideration. Infected cysts, or very large cysts are best treated at different times. Infected cysts can lead to infected breast implants, and this is always bad. The removal of a large cyst will allow the breast to heal, and resulting asymmetery can be addressed with the augmentation.