You have basically put a band-aid on it. Will probably split again but until then your ok. A damaged cork will effect your playing because it will eventually leak air.
I am having the cork on my tenor neck replaced today. Cork was ok but the glue dried and released the cork. Selmer didn’t do an adequate job since I used the original neck only once. Thought I’d try the stock selmer neck again and to my surprise with a Theo Wanne mouthpiece it sounded good so the neck cork is being replaced.
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