If they're on the map then they should show. If they're not on the map you need to use one that includes them as BaseCamp can't show what isn't there. Which map are you trying to see them on?
City Navigator North American NT 2019.2 .. I own nuvi 2595LM's... I have a county overlay I use on my Garmins to see county lines, but have never been able to figure out how to get county lines to show up on the map in Basecamp.. I use Basecamp to create my routes and then send them to my nuvi. I would find county lines very helpful when plotting my routes if I could get them to show on Basecamp.
I assume the overlay is a .img file? If so you should be able to view it in BaseCamp but as it can only show one map at a time it won't be if much use.