On the whole, and for Microsoft, yes. In its best years, Xbox made around $1 billion in profit. For a regular company that's an amazing amount of money, but it's not that impressive for Microsoft. Especially when you consider that Xbox makes a lot less most of the time, and can lose substantial amounts of money in the really bad years. Overall, Xbox has barely made any money for Microsoft over its lifespan, if it's even broken even. When Microsoft was counting on it to be a linchpin to grander plans that kind of weak performance is acceptable, but they've given up on that now, so Xbox's position has become a lot more in doubt.
You've answered the question here though. The Xbox division is entirely a footnote for the company. MS is massive (infinitely more massive than Nintendo, and a sizable difference larger than Sony). They could set the cash they spend on this division on fire, TDK-style, and it wouldn't matter to them.
Much like Hololens, this division is a patent farm. It's why they have Live (and their server farm for business), it's why they bought Minecraft, etc... It's good for companies to keep their businesses diverse, and a bit risky (in the sense that you're not betting on sure things, not the sense that you're betting the whole company on pagers coming back or something). Kinect, for example, was a big gaming failure (long-term, the first one's sales were insane). But the tech inside of it is going to stick around for decades, and MS is going to suck up all of those licensing fees and other revenue streams.
In fact, I'd argue that the division is going to get merged with the Surface folks, and just get Phil to run the software side while the Surface team builds the hardware. Those tablets (and the Surface Books) are insanely well-reviewed, and it's a good brand within the company (as is Xbox itself, much as GAF would disagree).
Hell, they changed their company logo (first significant logo change in the company's 20+ year history), and Xbox is featured as one of their 4 core businesses. Contrast that to something that they actually shut down (partly, rest to come I'm sure), the Windows Phone division. That division was noticeably left out of their core businesses when they announced the logo change, and here we are; it's dead. But Xbox getting shut down would be pretty awkward from a branding perspective.