I am currently 78hours in a play through of New Vegas, and I was wondering if buying the Ultimate Edition will allow me to use that save game in it.
Old saves totally work fine with all the new content. You'll continue on from wherever you are with way more items and quests to choose from.
The new quests get added to your PIP-Boy for the DLCs. For Courier Stash and Gun Runners Aresenal, all new items get added to player inventory and to the shops when you load your game.
Courier Stash might leave you encumbered, there's a lot of items that go into your inventory, including four sets of armor that when combined weigh a lot.