Should work just fine for running PhysX and basic output to a TV.
I think you will need to plug the TV directly into the GTS 250 if you plan on gaming with the TV, though.
Have you considered using a DVI => HDMI adaptor?
the gts 250 already got the HDMI build in
the tele is old school only got the RCA plug not the LCD TV with HDMI
the TV is not for gaming only for some youtube/old movie