I am not a lawyer, so do not take this as legal advice, please consult a lawyer if you want actual advice.
This said: Probably yes. EU data laws are mostly about private information, for example private chat messages, etc.
If you only store email accounts, you might get around the laws, but if you store anything like payment information, communication between users, etc, you effectively now have to follow EU data laws, which mean: You can’t give any third party (not even your government or hoster) access, you can’t store it in countries where the government might just seize your data (like the US), etc.
This said: Probably yes. EU data laws are mostly about private information, for example private chat messages, etc.
If you only store email accounts, you might get around the laws, but if you store anything like payment information, communication between users, etc, you effectively now have to follow EU data laws, which mean: You can’t give any third party (not even your government or hoster) access, you can’t store it in countries where the government might just seize your data (like the US), etc.