Since my Mathematica 10.2 installation CD only lists Windows Vista/7/8 the obvious answer is 'no'.
But I would like to know whether other Windows 10 users encounter the same problems:
I can't interact with Wolfram Demonstrations (they ask me to install the CDF Player although the latest version is installed).
Further, I can't access my printer from Mathematica (although other installed non-MS programs, such as OpenOffice Writer, allow this).
Also surprising: in text input sometimes the insert mode gets lost, as does the cursor.
Related MMa.SE thread: "Upgrade to Windows 10."
Earlier this summer (mid July) I had a similar problem in interacting with Wolfram Demonstrations. Windows 8.1. After installing Mathematica 10.2.
It was solved by waiting a couple of weeks, until a new installer had come out. Then reinstalling Mathematica 10.2.
Details of the problematic version: 10.2.0 5353456
My current, working, version:
I have since then upgraded the PC to Windows 10. No problems.