General releases of Windows do not support install on removable media. Variants are:
- SD controller emulating fixed drive (not for stick though - no suitable bus)
- Windows Embedded releases (build image for exact device from Embedded studio), have special driver for prolonged flash media life. All installs (like updates or drivers) only via building a new image for device.
From our hardware, you should be able to do that, but as per Microsoft you need to meet some requirements to install the OS, (check the comment above).
Now you may experience slow performance, the OS may run slower than normal, you can not install the apps, from Windows® market on the SD, (another Microsoft requirement )
If you want to extend the storage, install Windows (leave the current edition, upgrade to Pro, or upgrade to 10) and then use the SD card to put the user folders.
You can do this manually (but there is a lot of work involved) or you can use Data Igloo from Faronics
You can also forward other folder, registry keys and more, leaving the bare minimum on the Stick itself. Note however, that if you remove the SD card it might have bad effect in the system (It happened to me), and also SD card is not as fast as embedded SSD so it will take longer to launch