I’ve heard that it’s normal (expected?) that a chin implant will “settle” 1mm to 2mm over time. Is this true?

Depends what you mean by "settling".  Once there is final healing, movement of the implant is very unlikely.  However, over time there is a slight erosion of the bone under the implant.  It really doesn't have any functional effect, but it can be seen on Xray.  It is a normal occurance. It really isn't enough for you even to see a difference but it does occur.

  Hi, aside from the immediate post-op swelling which should be minimal with a submental approach...no, there is no 1 or 2 mm settling that occurs.  Be certain that you consult with Expert Chin Implant Surgeons. I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  
 Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut segments of bone).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  
Hope this helps.