I imagine that unless you are talking about reading some video files on your storage and playing those on the TV, no, it wouldn't work like that.
However, the Shield Portable does have a mini-HDMI port along with its micro-USB port. So you could just plug it into an HDMI port and you would have an instant mirror of your screen. In fact this is how you start up the "Console Mode" where you hook it to your TV and a charger, and you attach a Shield Wifi-Direct controller or a BT controller (or a wired USB controller I guess via a split charge/USB-OTG cable), and you have a nice way to stream your games from GRID, your comp, or native from the Shield to your big-screen TV.
TL;DR - No, wouldn't work. Don't need it though, you have an HDMI out on it.