[Arran]

 Are you asking about the 511 chassis being worth restoring or the matching speaker?, I would say that both are worth restoring if they are clean and in nice shape. That being said it will take some work, like cleaning out the original guts from the block condenser can and replacing the old caps with modern film capacitors, and possibly repairing an RF coil, and maybe replacing an audio interstage transformer. These sets are fairly simple electrically once you understand how they go together, the alignment and neutralization part is much easier then most superheterodyne sets of the early 1930s, basically they are like a TRF battery radio with the power supply built in.
 The speaker is a high impedance magnetic type like an old horn or set of earphones, to use a more modern dynamic with this radio would involve finding an output transformer to match it. It's easy to test though, place a 9 volt battery across the leads, you should get a loud click, if not the coil may still be good but the cable is not, so it's best to go directly to the back of the speaker with the 9 volt if the prior test doesn't work. Even if the coil is shot there are lots of early cone speakers out there for use with early AC sets that you can use with the 511.
Regards
Arran