Is it possible to detect (from code) what policy packs are enabled?

No, this information isn't sent to the running program.

Could a policy pack modify the stack in some way which the program could detect?

A policy pack could run a remediation step to change a resources inputs, and so the resulting outputs returned to the program might not be as expected given the inputs the program sent. So there are observable effects, but nothing as simple as a "did a policy pack run?" flag.