Can broken ferrite core be glued and used again?
If the transformer already has an air gap of ~1.5 mm, an additional glue gap of 0.05 mm will likely make no difference.

If the transformer was glued before you disassemble it, it should be broken right where it was glued, cleaned to bare ferrite and re-glued in the same way. It's likely to keep its performance close to what it was.

If you break the core in some random place and re-glue it, you introduce an additional gap. It depends on the transformer's and the SMPS's design how much it will affect performance.

I have unglued a few transformers putting a knife at some of the glue joints and hitting it with something about 100 g heavy. It succeeded in about half of the cases.