In the in between state of a society breaking down where people may respect a badge and there will be no follow up from authorities it might have a place...but bear in mind it will be impersonating a police officer. Its just that at that point in time it doesnt matter much so long as you are not doing anything bad with it.
I have done the reserve LE thing for a few years and i consider it a poor idea in normal times.
The phenomena you are looking for is a hesitation by LE, so they dont shoot you in a high stress incident. That is effect you are looking for. You are getting the effect by making the officer think you are a cop. I know you are never claiming to be one, but there is a reason the badge tends to work. This does not tend to put you in the best position afterwards. The officers may start out perceiving you negatively as a police wannabe or vigilante type. Is that fair, no, but it is a good possibility.
There are many things you can do to cause the hesitation on the part of the officer. Have good gear, have a holster and well maintained firearm. Practicing safe weapons handling procedures. Dress in a professional manner and be well groomed (yeah yeah, you beard guys can do it, just keep it trimmed). You carry a bloody gun to be ready to deal with the unlikely possibility that you will need to defend your life, you can dress yourself in a manner that presupposes a need to not look like a scum bad to the authorities. Basically you want to present an image to the officer that does not fit his concept of a threat. All those little things add up and he processes them, even if not on a conscious level. I also keep a blaze orange baseball cap in my go bag. My thought is that if the threat is down and the police are not on scene yet, putting that on would create an incongruous enough image to get him to slow down.
When I reserved I carried my shield on a chain in the go bag also. I dont know if I could have gotten it out in time to help in the time that it is really needed, an officer show up as I am shooting someone. At that point if I reach into a pocket, bag or inside my shirt for a shield he very well could shoot me. If he doesnt shoot you in that moment and it goes to talking I dont see the CCW badge as value added. The permit itself does the same thing and the badge may be a negative.
Its my $.02 G, take it for what it is worth. I dont condemn anyone for doing it, but I do not and would not recommend it to someone who asked me. A lot more people get arrested by the police than shot by them, and anything that makes your life harder on the right side of the arrest is probably not value added.
