from a business perspective, not really
How so? By doing this, it just makes people want to buy a different OS. When the Barnes & Noble Nook hit the market, almost everyone rooted it and installed Android OS, but even though this wasn't the intended purpose, it became popular to buy the Nook just for rooting it, thus, it had an unintended market, and Barnes & Noble continued selling them for this reason.
In the same way, if Microsoft were to not support Chrome, it would have the effect of forcing users to either use Spartan, find a substitute (Firefox, etc.), or to buy a different OS entirely. With all of these cases, Microsoft loses a portion of its market. As it is now, Microsoft also can't afford to lose any of its market because of a fair amount of disappointment that users had in Windows 8.