A lawyer's legal professional privilege is general, absolute and unlimited in time. Is that compatible with a tool that reads the firm's email? Yes, under the same conditions as any provider, plus a few requirements specific to AI.
A firm already passes privileged data through its email host, its practice-management software vendor, sometimes its accountant. The profession accepts this use of third parties, provided the provider is contractually bound to confidentiality and the lawyer stays in control. An AI tool falls within the same framework.
Where the data is hosted determines the law that applies to it and its exposure to extraterritorial legislation. For email covered by privilege, hosting in the European Union is a disqualifying criterion, not a preference.