Yes. A service animal is defined as any dog that is individually trained to do work or perform tasks for the benefit of an individual with a disability, including a physical, sensory, psychiatric, intellectual or other mental disability. As long as the dog meets this definition, it may accompany its owner on any premise or in any facility where members of the public or participants in services, programs or activities are allowed to go.
If it is not readily apparent why a service animal is accompanying you, you may be asked by a staff member on campus (1) if the animal is required because of a disability and (2) what work or task the animal has been trained to perform.
For more information you can read SUU Policy # 5.59.