Can a government submit a subpoena to Gmail asking for your emails? Unlikely, they would just answer that you are not a client of theirs and as such they don't have your emails.
Can they submit a subpoena asking Google to hand over all of the emails that your clients sent or received from your address? Sure they can. It's going to be a way harder sell to the judge and the reason and burden of proof will be that much higher, as it would essentially be closer to fishing or mass surveillance. But it's something that I can see passing for cases of national security or child abuse. Nothing I would personally worry about, but I understand if you want to wear a tinfoil hat.
Semantics and nuance matter.