Yes, as long as the bypass has its own route number. On the other hand, often a numbered route only incorporates a bypass. For example, State Route 73 is 135 miles long (217 km). It goes around Wilmington, Ohio, on the Wilmington Bypass, which is only 6 miles long (9 km). We could model the bypass specifically as a relation, but that would be analogous to making a relation for a city street. In situations like this, I’ve been content with tagging the individual roadways with the same name=* and wikidata=* tags. So bypass=* would go on the roadways as well.
I assume this proposal is partly motivated by the ongoing discussions about the criteria for highway=trunk in Poland and worldwide. I appreciate the effort to split out more descriptive keys for the various criteria that mappers have wanted to consider for highway=trunk, though this one feels a little more complicated than access_control=* because it’s based on local knowledge or intuition more than on-the-ground observation.
Incidentally, the Wilmington Bypass is built to Interstate freeway standards but doesn’t quite connect to any other freeway. It’s among the shortest “islands” of highway=motorway or highway=trunk anywhere in the U.S. under our newer connectivity-based classification standard. It’s an accident of history: as a condition for remaining in the city, a cargo airline insisted that the state build this bypass to improve access between the city’s airport and Interstate 71. Shortly before the bypass opened, a recession hit and the city fell on hard times, as DHL bought the airline and abandoned the airport.
We’ve gone back and forth about whether the rest of SR 73 deserves to be a trunk road, which would connect this highway=motorway island. The route connects Portsmouth to Oxford, which is just a small college town, so that would be a contrived reason for trunk. The main purpose of the overall route might have originally been for truckers to bypass the entire Cincinnati area on their way to Richmond, Indiana. Nowadays, it doesn’t do a very good job of that either compared to other highways in the area. Or maybe it’s just to connect Portsmouth to Middletown, which would be more plausible, plus an extra dangling segment to the west. Either way, we haven’t felt a strong need to emphasize either the route’s connectivity or its bypassing function.
This is one of several states that loves to build bypasses around small towns. Freeway names are almost never signposted, so essentially the name of the freeway is whatever the construction project was called. A bypass usually has “Bypass” in the name, even if it doesn’t end up with its own route number.