Yes, you would, assuming you’re still positive earth, but you’d also need to make sure that the cigar lighter is well insulated from the car’s metalwork.
I changed to negative earth, changed the cigarette lighter unit for a modern one and fitted an in line fuse and hey presto. I also have a parking light I plug into the cigarette lighter unit.
Tried modern plugs and they fit (been using a Halfords tyre inflator, with the wires switched as a precaution, for years) mine’s a late model 67, perhaps they changed the sockets?