I've just got the same unit. Firstly you want to download and install the OpenStreetMap maps from TalkyToaster which are much better than the Garmin basemaps.
In answer your question I'd say that a route that you plot in [say] MemoryMap and download to your GPS is merely a list of waypoints and are therefore completely unrelated to the map the're shown on. Think of a route as an overlay. You can show it on top of any map or none at all (such as when used on a GPS not capable of showing maps). The GPS will simply direct you to the first waypoint, then the second, and so on until it reaches the last one. The map is simply there for your reference.
When you're talking about road routing (i.e. turn by turn directions) there is a relationship between the route and map as the GPS uses data from the map (i.e. the roads) to determin your route.
The OpenStreetMap maps are routable so you can use your HCx for road routing once you've installed the maps on the memory card.