It depends on the enclosure. Some act as JBOD (just a bunch of disks) and present each drive as a separate disk to the computer over a single USB connection. Some do some form of RAID and allow you to combine the drives into a single volume.
Whether the router is capable of identifying the multiple disks, I don't know. Most routers run Linux, and Linux can handle multiple drives over a single USB port (as if using a USB hub). So I could assume the hardware is capable of recognizing multiple drives connected to a single USB port. But whether the network sharing software is set up for that possibility is anyone's guess. You'd have to try it to be sure.