Does playing first person shooters make a better real life soldier?

Most shooters, probably not. But sometimes I wonder if Arma 2 and Arma 3 teach players some real world military skills. The company behind these games (Bohemia Interactive) also works on simulations for the defense industry and it's clear that they applied this experience to Arma 2 and Arma 3.

I heard that the US army used to train Bradley crews using an Arma 2 mod. From playing the game, I can see how this would be viable. In most games, tanks are just programmed to be easy for one player to control. However, in Arma 3 a tank has a commander, gunner and a driver like an actual tank. So it teaches you the absolute basics about how a real life tank crew is supposed to work.

Probably not yet. Even if there was a VR headset and suit setup that made you feel pain and felt/heard explosions at dangerous levels, it would not be the same. You won't have the genuine fear of death and won't experience the same level of psychological trauma. Maybe some day there will be a brain interface that allows you to re-live or experience combat real time. I hope Elon does not read this. I could see a not too distant future VR setup that makes you better at shooting moving targets and controlling drones that assist you. Some games already make an attempt at this.

Does it make you a better infantryman? No. Is the type of person that plays games probably better at figuring out different mechanics of the various systems in use by the military? Probably.

You can't generalize "soldier" into one MOS(military occupation). While the main goal of the military is to fight wars and conflicts, that requires many different skill sets and different job requirements.

No, it probably makes you take unnecessary risks due to a false sense of bravado

Absolutely not. The Arma series might be an exception for a limited set of aspects, but that falls more into the "military simulation" category than what most people associate with an FPS.