Yes. This would be extremely helpful for experimentalists who spend a lot of their time pointing out, for example, that one's new theory can't violate the equivalence principle by very much at all. Similarly, it would be helpful for people planning new experiments to know whether or not their proposed experiment will probe new ground (i.e. CERN's anti-hydrogen experiments are of intense value for spectroscopic studies, but existing experiments [1] show that antimatter, at the 10^-8 level or better, obeys the equivalence principle and therefore will reliably fall in every experiment of which CERN is capable.).
As a sibling comment points out, it is difficult to implement the markup that spans the space of all possible theories. Kostelecky's parametric Standard Model Extension offers one avenue to do so.
One could implement such a test as a checklist, too, which might already make a difference.
