Is it possible? Yes. The battery pack you describe holds 4.8 kWh. If you're using an inverter between the battery and the TV, you're going to lose some of that to inefficiency of the inverter, but not much.
Back when inverters were expensive, heavy, and generally junk, me and my wife set out on vacation. I had a mountain of work to do, and thought to myself that I could set up a PC in the back of the van and knock out some work while it was her turn to drive.
Here's the part important to you -
I simply constructed a DC-DC converter that so that I got about 150V regulated DC from our 12V system. It worked great!
Why? Because almost everything uses a switching power supply, and the first thing that a switching power supply does is rectify the incoming AC and make it DC for a DC-DC converter. What a sweet deal, no pure since wave needed!
But, there is a complication. Since you are working with high voltage DC rather than AC, the original fuses don't work properly. Should a fault happen, they like to carry an arc. So, you're forced to give up your 25 cent fuse and replace it with a larger one of the same current rating, but made to break DC. They used to cost about $4.00.