We have some Siva Vishnu temples in which both Siva and Vishnu are worshiped. temples like Sankaranarayanan koil have both deities in the sanctum sanctorum. In my town at one of the local hindus temples, the main deity is krishna, but there is a Siva linga also and all major Hindu religious festivals like siva ratri are celebrated.
These would be examples that don't belong to any vaishnavite sampradaya, but vishnu or one of his avataras is being worshiped.
Mere co-location of Vishnu with an anya-devata doesn't exclude following vaishnavite sampradaya - at chidambaram govindaraja (vishnu) is co-located with nataraja (Siva) but there ia an old joke that iyengars on entering the temple complex would walk with averted eyes until they come to the vishnu temple, do their worship and walk out with averted eyes.
The second part of the question is not necessarily about anya devatas - the question is whether an agama accepted by vaishnavites is being followed.