In the EU, e-mail addresses are personally identifiable information. It's not clear that an append-only log with no expiration or means for individuals to delete the content will even be legal in many EU countries.
In practice, no, you can't demand to be wiped out from the internal database if you creditor. You probably can prevent them from publishing a debtors' list with your name, though.
Even then, as pointed out by others, this does not preclude the user from withdrawing consent to continued use of the information.
It may or may not become a legal problem. But they really need to consider the privacy implications and have lawyers that actually know the relevant national laws throughout the EU member states to evaluate it.
But personally, regardless of legality, if Google implements this with the degree of disclosure of e-mail details, I'll find another operator that isn't implementing this proposal.