It's kind of the wrong question, frankly.
Of course I'm online when I'm playing an MMO or a multiplayer shooter. And one could answer "always" simply by nature of the fact that many people who use the Internet for gaming in any way- whether it's playing World of Warcraft or downloading large game files from a site like Good Old Games- use an "always on" Internet connection simply because that's the way most broadband Internet connections work.
My preference, however, is to use firewall software like Zone Alarm and strictly regulate what software can use my bandwidth pipe to call back to base, download patches, and so on (thank you, printer driver, you work just fine without trying to patch yourself on a daily basis...) This is the kind of choice that shouldn't be taken away from an end user on a cavalier basis.
So, yes, maybe I am online, by various definitions, when I'm playing a PC game; that doesn't necessarily mean I'm okay with software I didn't choose being online at or over my shoulder simultaneously.