Possible yes.
Reasonable I'm not quite sure.
To me, Alloy shine at finding unknown unknowns, i.e. pitfalls, in your specifications.
Once the specification is fool-proofed using Alloy analysis, I don't see the point of encumbering your program with unnecessary translations and analysis steps. It's not only error prone, but you might also find yourself limited with the scalability of the analyzer if the traces you want to validate are substantial...
But again, it's doable. So if you want it, sure, do it ... :-)
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