Can a Gmail connector let Claude analyze all past emails with a client without manually printing/uploading them?

The question was raised about whether, with a Gmail connector, you could point Claude at a specific client and have it analyze every email ever exchanged with that person -- summarizing the relationship trajectory, how fees have changed, flagging problematic behavior, or even emailing you at night with findings -- without the manual step of printing and attaching emails. The group agreed this would remove the manual effort described in the prior email-drafting example, though the discussion did not confirm exact connector capabilities or limits in detail.