lol, you don't need a fully built transmission. A shift kit and some billet servos will do just fine. Unless you plan on dogging the shit out of the truck, you'll be ok. My stock transmission was fine with my tvs1900 and a host of mods (LS7 TB, Headers, Exhaust, intake, tune, etc...).
When we blow the Burban, im only doing a shift kit and billet servo on it. We're only blowing it for added towing power and to get the beast up to speed a little quicker.