I believe the car will stay on even without the key present. When cars are stolen through relay theft, the thieves don't have the key (they just extend the signal from the key inside the house). Therefore, they just can't stop the car because it won't start again if it can't sense the key is nearby. Essentially, if you start it and put it in the pouch then it should stay on but it might flash up some warnings that it can't detect the ley anymore. I wouldn't personally advise it, I don't really know why you'd want to do this either - but, in theory, it could work.