At least right now, Cloud will only run Universal Windows Platform apps found in the Windows Store. Try to run anything else and you'll get a stern warning. Most likely, this is to court schools and other institutions who see Chrome OS' lack of native apps as a security advantage. Educators may be more likely to stick to Windows PCs if they know that kids can't infect a machine with malware or install an unapproved game. It's possible that Microsoft's "Centennial" bridge (which brings Win32 apps to the Windows Store) should work, but there are conflicting reports about compatibility.
It's not certain when Windows Cloud might show up. With that said, there are mentions of the OS in current Windows Insider preview releases. That suggests Microsoft intends to release Cloud relatively soon, and could ship it (or just talk about it) when Windows 10's Creators Update arrives in the spring. The timing would certainly be right. Schools tend to prepare their tech budgets months before the start of classes, and Microsoft will need Windows Cloud-equipped PCs on the market very soon if it's going to lure the educational crowd away from Google's offerings.