Possibly! I'm not sure it it has ever been accomplished. Diffusion tensor imaging (DTI) with tractography would probably be the best method to to this.
Our lab is able to visualize white matter tracts in the brain to a diameter of approximately 2 mm. A quick search revealed at least one article using DTI for facial nerve (PMID: 17031835), but I think this was intracranial only. In other soft tissue, DTI has been used to map nerve fibers around the prostate (PMID: 22748877).
Potential complications I can see would be false "fiber tracts" caused by nearby muscle fibers, also motion errors within and between diffusion gradient directions. You might need to design some MR-safe mouthpiece to keep the buccinator/masseter/etc. motionless.