Can a fat transfer be made to the throat region to obscure a prominent adam's apple?

Shaving the tracheal prominence surgically is a much more refined and predictable procedure than fat grafting, which may create irregularities and fullness in the neck.  With modern techniques, a tracheal shave is safe and the scar is easily camouflagable.  

I would not recommend doing fat injection as opposed to a trach shave. Reducing the Adam's Apple is a safe procedure with limited downtime in the right hands. If you are wanting to avoid any risk to the vocal cords you should go to an experienced surgeon who looks at the vocal cords with a camera during the procedure. 
Fat transfer is a great procedure for the face, but it often takes multiple procedures to get the desired result. Injecting above the adam's apple enough to camouflage the bump will likely result in a full neck that blends into the chin which is not aesthetically ideal. 
Best,
Sarah Saxon, MD