I don't think this will work, even though both windows 2008 and 2012 are supported, BI 4.1 wont be in good shape after OS upgrade, its good idea to setup new installation on 2013 and move your content from 2008 machine.
If you are proceeding with scenario of upgrading OS with BI 4.1 on ,do please share your results.
Thanks
Pavan K