Running CodeGen/Generic tests on different targets

Is there a simple way to override the target triple used in when running
the generic codegen tests? I would expect that passing a value for
TARGET_TRIPLE to make, as below, would do it but none of the tests
appear to use the target_triplet variable generated in site.exp.

make TESTSUITE=CodeGen/Generic TARGET_TRIPLE=msp430-none-none check

-Ken