No, because in those cases you're still a user of gmail. When you tell people your email address, or send people email, and it contains "@gmail.com", you're still implicitly advertising for Google. From Google's perspective that's still worth the few KB per day of bandwidth and 1GB storage (which the vast majority of people never use the entirety of, anyway) they're giving away.

But when you use gmail accounts as file storage, you're both a higher-cost user and also doing nothing to further Google's ecosystem (since the email address itself is probably not being used for genuine messaging at all).

It's not analogous at all because Google intentionally provided interfaces for those clients and even instructions for using them.

An analogous situation would be if someone reverse engineered the Google Maps API and provided their own app that showed maps using the Google Maps data.

Google explicitly allows third party email clients to work with Gmail, so no that hypothetical does not apply to this situation at all.