It is possible, many have done it and three have come to me to get it undone. I restored two cars to factory and refused to help with the third one - as it was such an abortion that I wanted nothing to do with it.
Why did they want it taken out? Because no starts are hard enough to troubleshoot with these cars, adding another layer to it by putting in such a mod does not help.

I've given up trying to talk people out of this mod, if you want your "super cool push button start", fine, do it. Just keep in mind:

1) No-starts with a Crossfire can be hard to diagnose, many come to the forum for help. Those of us who help have NO CLUE what was done to your car and our advice will not include knowledge of that modification. You are largely on your own.
2) Given number 1, I'd suggest you only add the mod IF you can do the mod yourself AND troubleshoot any issues yourself OR if you have a local person you trust to install it and be there for you when no-starts occur.
3) A push button start defeats the locked steering - making stealing the car way easier.
4) Adding push button start DOES NOT eliminate the role of the SKREEM in starting the car, you simply hide the black ring around the ignition switch behind the panel and tape an RFID chip in the key to it, so the SKREEM will authorize a start. If your SKREEM fails, the push button start kit will not enable the car to start.
4A) One of the tuners who does SKREEM repairs can put in a push button start AND SKREEM start-enable bypass, you could go that route to get around a SKREEM failure - but why not save the money and just have them do the bypass?