It depends, in my opinion. For your Oracle read-only database, is this physical standby being managed by Oracle Active Dataguard? Those are, by definition, read-only as you mention. From your primary database, you'd be able to replicate the SDE user schema (and other schemas) to the secondary / read-only standby... thus allow you to make an ArcSDE connection. But, you wouldn't be able to perform inserts/updates/deletes by way of adding feature classes, re-calculating spatial indexes, or deleting relationship classes. These types of operations issue SQL to modify objects just like any other SQL command you might issue on another schema's set of objects. In summary, I think SDE would "work" as far as being able to connect but that's it.