Every S197 I've seen with twisted axle tubes was running LCA relocation brackets. UPR's 2010 GT, which is a 4,000# porker, runs 9s with 1.35 short times and it doesn't have welded axle tubes.
However, if you want to run the relo brackets, you should definitely weld and brace the tubes as much as possible because the relocation brackets give the LCAs a longer moment arm on the axle tube, which means that it is easier for the axle tubes to twist within the center section when using relocation brackets.
If you're like me and you prefer a simple explanation, it's like this: it's easier to loosen your lugnuts with a 2 foot long ratchet than it is with a 6" long ratchet because you have more leverage on the nut. Well, the relocation brackets space the LCAs away from the axle tubes which gives the LCAs more leverage to twist the axle tubes with. No bueno.
For those of you with concerns about your axle tubes, UPR offers these axle braces:
http://www.uprproducts.com/mustang-888-rear-end-braces.html