If you only need to use Python without any ArcGIS tools this will work just fine. However, you will be completely unable to use Arcpy from that separate Python.
I have successfully worked around this with the Enthought Python Distribution by starting EPD with a bat script that adds ArcGIS paths to the PYTHONPATH:
:: start EPD32 python prompt with arcpy available
@echo off
set EPDPATH=E:\python27_epd32
set AGSPATH=D:\ArcGIS\Desktop10.1
:: save paths
set PATHENV=%PATH%
set PPATHENV=%PYTHONPATH%
:: set paths EPD with access to arcpy
set PATH=%EPDPATH%;%EPDPATH%\scripts;%PATH%
set PYTHONPATH=%PYTHONPATH%;%AGSPATH%\bin;%AGSPATH%\arcpy;%AGSPATH%\ArcToolbox\Scripts
cmd /c %EPDPATH%\python.exe
:: restore paths
set PATH=%PATHENV%
set PYTHONPATH=%PPATHENV%
:: delete variables
set EPDPATH=
set AGSPATH=
set PATHENV=
set PPATHENV=