Just a quick question:
What is this threaded hole on the back of an old alnico woofer for?
Is it a vent?
Shine a small flashlight up in there and see if it is a through hole or not. Better yet, put your lips against it and blow. If air blows through, then it is a vent. If it is a vent and you blow hard enough, the woofer cone should move some.
If it is not a vent, then it is some sort of manufacturing hole, part of the manufacturing process.
If it's not a vent, then yes you may insert a screw. I'd suggest using a non ferrous screw. I.E. brass.