The short is "no," but the longer answer is more complex. Standard breast reduction (reduction mammaplasty) surgery generally involves an incision (and later a scar) around the areola (the pigmented area around the nipple), down the front of the breast (vertical incision), and (sometimes) along the fold or crease under the breast (the IMF or inframammary fold incision). However, not every breast reduction involves all of these scars. Some breast reductions involve simply an incision around the areola, but that is not usual. Breast reductions also can be done with tiny incisions by using only liposuction, but that is even more unusual.
The incision pattern is determined by the needs of the patient and the size and shape of the breasts. Very "droopy" or ptotic breasts can be lifted by altering the skin only. If, in addition to being ptotic the breasts are overly large, then some breast tissue must also be removed. This is done to relieve neck, back and/or shoulder pain related to the large size of the breasts. The incision pattern can be the same either way. It is generally called a "Wise pattern" or "anchor pattern," the latter name coming from the shape formed by the combination of the incision around the areola, down the front of the breast and the IMF incision. Another possible incision pattern is the "lollipop" or what we call "circumvertical", which is a combination of the incision around the areola (circumareolar) and the vertical incision. This is also called a "vertical reduction mammaplasty."
One other option is a breast reduction done with a combination of a periareolar incision and an IMF incision, leaving no vertical scar. This can leave a lot of bunching at the IMF incision which can compromise the result, and it is not the preferred technique of most plastic surgeons.
For patients who have breasts that are larger than they would like, but do not have much "droop", liposuction alone may be a reasonable option. This can be done with small incisions under the breast, leaving scars that are virtually invisible.