Officially, no, you can't use this application on Windows 10 as the system requirements on the Google Input page (since it belongs to Google) clearly states that the compatible operating systems are the following ones: Requires Windows 7/Vista/XP (32-bit/64-bit). However, unofficially, you can go ahead and download the setup package to install it.
If it's just a standard IME, you will have the possibility to install it on Windows 10 as well.
