PS C:\> taskkill /F /IM python.exe
SUCCESS: The process "python.exe" with PID 14896 has been terminated.
PS C:\> python
Python 2.7.8 (default, Jun 30 2014, 16:08:48) [MSC v.1500 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import arcserver
>>> import arcpy
>>> arcpy.ProductInfo()
u'ArcEditor'
Not sure what's up here. I've had ArcGIS Server and ArcGIS Desktop installed simultaneously on my machine for a long time (10.1.1, 10.2.2, and now 10.3.1). The above always worked fine to make sure arcpy scripts were using the ArcGIS Server license instead of grabbing a desktop license. After upgrading both to 10.3.1, arcpy seems to completely ignore the server license and always look for a Desktop license.
Edited to show that no other module or process had already imported arcpy.