The treatment of unsigned roads may depend on the highway system.
Unsigned Interstates are presumably always gonna be freeways and are unsigned due to some decision by the state DOT, not always because of their functional characteristics. For example, the freeway portion of US-90 Business in the New Orleans area
is unsigned Interstate 910 — LaDOTD doesn't sign it as such because they're putting a lot of weight behind its part as one end of "Future I-49". LaDOTD's functional class maps shows that portion as a "Principal Arterial - Freeways/Expressways", and it's a freeway. I feel the AASHTO wouldn't designate a road as a current Interstate unless it was either up to standards or grandfathered in (if, say, the shoulders are too small).
Lightly-signed US highways are still US highways, even if it's kinda hard to follow them just using roadside signs. There's an interest in having them labeled consistently, especially since they'll be Major Highways on either side of the metropolitan area. Downgrading a road as it travels through an urbanized area is one of the things we want to avoid.
Unsigned state highways, on the other hand, will differ by state. In my experience even the most insignificant "state highways" are still signed, but still, it depends. It may be valid to say that unsigned state highways should be set as Primary Street at minimum or maybe not even considered as state highways at all, I don't know. But maybe we just shouldn't worry about it.
Related but different: State and US highways designated "Connector" should not be downgraded in the same way that "Business" and "Alt" routes are, since they typically serve to connect a main route to an Interstate or other major arterial. Likewise, "Spur" routes which are used as connectors should also not be downgraded — typically in state highway systems which do not designate "Connector" routes, like Louisiana. Possibly "Truck" routes should also not be downgraded — since they're presumably necessary for long-distance travel for trucks.