No, it's not the functional equivalent. My phone is not a web browser, and it's broken to try to treat them the same. My web browser's back button never drops me into Office, and it never dumps me onto my desktop. It moves through my web browser's history. It doesn't try to build some awkward linkage between what I've done in my web browser and what I've done outside my web browser.
The idea that you have a linear sequence of "actions" across all apps seems pretty weak in a multi-tasking environment.
If all your applications exist in the browser (say you're a lover all Google apps) then yes the back button in the browser might drop you into your spreadsheet, your email, etc.
Google has simply extended the concept from web apps to regular apps -- and that's hardly a big stretch -- especially when all your regular apps can link to each other.
Actually that's an interesting point, because Google Apps don't do that. If you're in Gmail and you open a spreadsheet, it opens in a new Window/Tab, so that it has an independent history. Ditto if you click on a link in an email. This approach gets you separate histories for your apps. You don't get an awkward single history that links across your mail and spreadsheets and random websites. You get separate histories. The exceptions are when you choose to manually enter a new URL, or if you hit back enough it will take you out of Gmail into whatever you were doing before.
The "desktop" you're referring to is the functional equivalent of your web browser's home page. So yeah, the browser does take you there.