In a word, no. The autoboxes in this generation of Audis are made of putty and struggle to cope with the stock torque, let alone modified. This isn't just me being biased either - they really are terribly unreliable. Have a look in the A4 and A6 forums on
http://www.vwaudiforum.co.uk. At one stage probably half the threads were on gearbox problems
The tiptronic is worst, but the multitronic fares little better.
There are two main problems with them, which
may be solvable with enough effort:
#1 Audi say the boxes are sealed for life and never change the fluid, so it ends up getting burnt and causing the clutches to slip.
#2 The programming on the TCU is set to shift really smoothly, slipping the clutches as it goes and burning the friction surfaces. See point 1...
If you must get an auto then look for a low mileage one (60K tops) and have a dealer check the fluid. If it is still like maple syrup then its fine. If its dark or smells burnt the box is toast, and you should run away. If you really like a particular car then its worth spending an hour's labour with Audi to save yourself a £3-4K bill later!
If you do find a good one get on Google and look for a 'tip chip'. Some US-based tuners can supply this and it speeds up the shifts which in turns reduces the burning of the friction surfaces and the oil. Oh, and put fresh oil and filter in it (Audi will tell you this is unnecessary - ignore them and go to a specialist if so). Oh, and also look on Fourtitude.com for a mod to increase the solenoid pressure too.
None of this will stop it dying eventually, but it might prolong its life past 200K if you're lucky. My A8 made it to 188K before it died, but I was lucky.
Or get a manual
Footnote: BMW use the same 'boxes as Audi, but they don't die. Why? Harder (ie sporty) shifts and scheduled fluid changes...