I bought this phone in the Mauerpark fleamarket. It looked really cool and old. I wired up a new wall plug for it and it works fine.
It turns out that it probably isn't that old, after all. This page (German, English translated) says that the W48 was made starting in 1948, but the DDR continued to produce them until the 1970s. Wow.
The main indication that this may be an older phone is the wire to the handset is straight, stiff, and cloth-wrapped instead of curly and plastic wrapped.