Does ASI R6 help you at all with your civilian law enforcement career? Or is it just cool thing you can say you did on your resume?

As a rule of thumb your military certs have no application to civilian employment unless they are civilian certs. However, the experience you gain while doing a job using your military certs and training can transfer very effectively.

It helped me as it showed experience and that I had been trained to work in the field. It didn’t help as far as a civilian cert or license. So I didn’t get credit for promotion and it didn’t make a difference that I know of for my lateral.
All that was a few years back but I doubt much has changed.

I was a police officer for about 3 years during a break in service. I will say that they really don't care. The issue is that they can't validate the credentialing. If you think you are going to walk into law enforcement with any expectation as being treated better than the new guy that doesn't know anything then you are going to be in for a rude awakening.