Maybe.
Smaller countries very often lack resources to "aid" it's banks during a crisis.
Georgia, for instance, will have a hard time supporting BoG/TBC since these banks are too large for government coffers.
And then we have Cyprus .... 🙄
So, simple strategy: Do not exceed the maximum insured amount. If that amount is too low (for you), either look elsewhere, split the amount between different banks of the same jurisdiction or put your money in securities (bonds, stocks, ETF,. mutual fund). For the latter option, make sure that these assets are separated.