Can a chin implant "pull" your cheeks forward to give the illusion of a slimming effect?

By placing implant in well defined soft tissue pocket on top of the bone, there will be no movement of soft tissues around (cheeks, neck). However, visually it will change the relationships which may be seen as surrounding areas have change as well. Without in-person evaluation it would be hard to give you more "elaborate" evaluation. Good luck.

 No, a chin implant augments the chin, and does not pull the cheeks forward. Chin implants offer a three-dimensional augmentation of the chin area when there's a weak and recessive chin profile present. For more information  and many before-and-after examples of chin implants, please see the link and the video below

A chin implant will have no effect on what lies above it, meaning it will not have a direct slimming effect on the mid face/cheeks. It can have some beneficial effects, however, on what lies beneath it or the submental region. By pulling the soft tissue chin pad forward it may provide some slimming effect on the neck below it although it will be relatively minor.

 Hi, I have performed many facial shaping procedures, using dermal filler or silastic facial implants including 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.   Specifically addressing some of your questions:  While a properly placed chin implant corrects a weak chin by providing forward projection to the chin, as described above, it has no "real" affect on the other facial features.  A balanced chin will make the lower face more noticed which in turn may make less than ideally shaped cheeks less noticed.   A typical projection for a silastic chin implant in a man is a size medium EAC implant with 0.5 cm or 5 mm projection.  You mentioned 2 cm which would be 20 mm's.  I know of no application for such a huge implant, nor would it be able to be placed properly within the anatomical limitations of the sensory nerves along the jaw line (mental nerves). Following my beauty principles, men look chiseled and handsome with angularity in the cheeks, chin and mandibular angles.  The following procedures would create a more ruggedly handsome face.
Cheek augmentation with cheek implants to add angularity to the cheeks and mid face.  Liposuction can be combined to reduce any excess fat to further shape the cheeks and face.
Chin augmentation, using a chin implant, to add projection to the chin creating harmony and balance to the lower face (discussed above).  
Augmentation of the mandibular angles using a dermal filler (jaw implants have too many unwanted side effects IMHO) to add volume, angularity and flare to the jaw line.
Hope this helps.