Yes it will run Windows 10, and no it won't run the 64 bit version.
Yes it will run Windows 10 32 bit.
The Intel Compute Stick comes with Windows 8.1 with Bing. It is also currently eligible for a free upgrade to 32 bit Windows 10 home edition which will download and install if you click the windows icon that will appear on the task bar. Windows 8.1 with Bing is given to manufacturers of 32 bit tablets and other low end Windows devices for free or nearly for free by Microsoft.
Why It Will NOT run a 64 bit OS.
First reason is the compute stick has a 32 bit UEFI. The OS size must match the UEFI size, so your 32 bit UEFI runs only with a 32 bit OS. 64 bit UEFI restricts you to a 64 bit OS. The second reason is the built in SSD is only 32 GB. 64 bit versions of Windows take up a lot more space than the 32 bit versions, so even if you managed to squeeze the OS onto the 32 GB drive you would have no room for applications. It just would not make sense.
The 32 bit OS works perfectly well for most uses, but this computer is not a gamer's machine. Still considering what you get it is well worth the price.