You would be putting yourself and others at risk by making believe you had a real gun. You can believe that any encounter with a LEO will result in the officers having a very unfavorable opinion of you and what you were attempting to do. (It's better they carry a real gun)
As a retired LEO, I was never bothered by the guns I could see, but anyone 'Acting' caught my attention every time.
I am and have always been in favor of Open carry, but would be suspicious of anyone I saw with a make believe gun.
There are very good repo type fakes on the market, but why would anyone carry them just to see what the reaction would be.
I would first wonder If they were playing with a full deck...
There are officers who either disregard the laws or are not informed about the laws. The easiest way to talk with the officer is before he decides you may be a nut with a water pistol.