Does the alternative stack make Script Turing complete?
You may be interested in a post I wrote. I wrote a Turing Machine (by utilizing the two stacks) and made a test transaction.

Basically if we assume that our program will halt, then it requires only a finite number of instructions, which is supported by the Bitcoin script. Unfortunately the Bitcoin script VM only allows a limited number of operations to be executed so only very short programs can be written in practice.