Can I query a partial network when all of the instance nodes under an edge node are unavailable?

It depends.

If all of the instance nodes under an edge node become unavailable, then the edge node will also become unavailable.

An unavailable edge node that is not included in a query will have no effect on the query - but if the unavailable edge node is required by a query, then the query will fail.

Note that an edge node can be made highly-available by attaching multiple instance nodes to it.