AFAIK the box will fit (so long as you use the 01E, some later cars use a different box)
The problem will be matching the rear diff ratios. You'll need to find out the ratio of the front diff in the box, and then see if theres a B5 rear diff that matches it.
You can also use an S4 box, but again you'll need a matching rear diff (which iirc you can get from a 2.6 Quattro, as well as the S4)
As for fuel savings, IMO its going to be minimal. The majority of the fuel consumption on the motorway is aerodynamic drag, friction from the tyres etc. Slowing the engine from 3500 to 2900rpm is not going to change much, and if you drop it too much you end up below the boost threshold and economy disappears.
Most petrol 6 speed Audi boxes are designed to have a better spread of gears, with the top cog not being THAT much different. 80mph in an S4 is about 3000rpm, whereas 80mph in a TQS is about 3500.
As a mod to gain an extra gear and perhaps reduce engine noise slightly on the motorway, sure, but i wouldnt go fitting it for fuel savings, as you will be dissapointed.