Can augmentin (amoxicillin and clavulanate) cause a non-allergenic rash if pt has virus infection due to viral antibodies?

Yes: Yes, but it doesn't depend on a viral infection. Many meds, including antibiotics like Augmentin (amoxicillin and clavulanate) (amoxicillin/clavulanate) can cause bothersome rashes like contact dermatitis (an allergic reaction) or urticaria (hives). Less frequently & much more serious, it (like other meds) can cause a skin reaction called erythema multiforme and stevens-johnson syndrome requiring immediate medical attention.

Yes: Any antibiotic, including augmentin, (amoxicillin and clavulanate) can cause a rash - most of which would be considered allergic in nature but could still occur for undefined reasons even in the presence of solely a viral infection.