I do not have the spare tire mount in question, but I have a lot of experience with different bike racks. All the rack manufacturers have a dimension chart that shows the distance from the hitch pin to the rack when it is folded up. It also shows the distance when extended normally. That distance is probably the main determinant for whether a particular rack will work with the spare holder or not.
In the picture above, that distance will apply to where the recovery loop is attached. Doing my best guess based on the picture, the Saris MTR I have now and Kuat Transfer I used previously would not fold up with the spare. They’re also pretty heavy and I would be concerned about hanging that much weight that far from the actual hitch.
I previously had a Swagman that had a very long arm extending from the hitch that could work, but again, the weight would be a concern to me.
If a cargo basket is an option, the Rhino Rack X-Tray has thru axle mounts that you could use to carry the bike. I’ve also thought about throwing a full size spare up there since I carry more than one bike pretty frequently.
