What does CREATE ASSEMBLY do with the registered dll?
The bits are copied into the database where you call CREATE ASSEMBLY or ALTER ASSEMBLY.

The path you select in Management Studio is only a convenience for it to read the file and dump out the bits into a varbinary(MAX) value (hit the Script button in that dialog to see what I mean).

This also means that the assembly is "carried" with the database if you do something like backup/restore on another server.