I guarantee you that "OBDI to OBDII" adapter is complete and utter junk. Do not actually try to plug it into a car. Don't have to believe me either, you could just take out the screws holding each end's plastic case together and crack the thing open and trace which wires are connected to which pins. 100% guaranteed the pinouts won't make any sense and, in the worst case, will connect 12V to something it really shouldn't be connected to.

TunerPro can technically do OBDII as long as you have an appropriate ADX but it's not very good at it. There are better alternatives for OBDII vehicles. If you just want general OBDII information, I personally use OBDLink SX for that purpose. If you want GM-specific OBDII information and/or want to perform more advanced procedures (bleeding ABS, energizing solenoids, etc) then you may want to consider investing in a Tech 2. A stock Tech 2 card will handle any GM vehicle from 1992 to 2013. An alternative program exists which will handle 1981-1997 as well.

If VATS is the culprit it will be insanely obvious. Every vehicle I've ever interacted with--GM, Chrysler, Honda, Toyota, etc--has a visual indicator on the dashboard that's insanely obvious and tells you explicitly that the key inserted doesn't meet the requirements to satisfy the anti-theft system. All three of my C4 Corvettes has that indicator. The Chrysler PT Cruiser has that indicator. The '14 Honda Civic has that indicator. The '15 Toyota Corolla has that indicator. That's nearly 25 years of vehicles from multiple manufacturers who made sure to put a super obvious visual indicator on the dash to indicate the state of the anti-theft system. As such, while I don't know anything about the 2003 Avalanche, I'd bet dollars to donuts that there's a dash indicator for VATS. So if your theory is correct, you won't need any scan tool whatsoever to prove it.

Best of luck!