Will getting a tummy tuck cause the breasts to sag?

The best answer is "it depends."  If the surgeon goes high up on the abdomen to the ribs to tighten the skin and muscles (generally this is good) and you have a lot of upper abdominal laxity I have seen the breast folds pulled down slightly.  This is most common in patients who have lost large amounts of weight (i.e. over 50lbs.)These are typically small changes, and can affect the breast implant incision, and I haven't see it make a breast actually sag.

Undergoing an abdominoplasty should have no effect on your breasts at all.  It might lower the fold of the breast a tiny bit, but that is it.  Your breast folds sit up on your rib cage, while an abdominoplasty stops at your ribs itself.  I hope this helps.