It will almost certainly be fine. It's likely that the winding broke where it connected to the terminal, as the primary of the transformer is quite thin wire.
It is just possible that the 0 - 120 V winding was larger diameter than the 120 - 240 V winding, as your amplifier would take less current when running on 240 V, so smaller wire could be used. However, on small transformers that would add to the cost of construction, and would only save a tiny amount on the wire so it wouldn't be worth doing.
On larger transformers, it's quite common to have two 120 V windings, and to run them in parallel for 120 V supplies, and series for 240 V supplies. On those, only using one primary winding could cause a problem at maximum load. As whoever made your transformer didn't think it was worth having two separate windings, they probably used same wire for all of the primary windings.