Can you use a model rockets secondary charge to ignite another model rocket engine?

At my school we have AFJROTC and in ROTC we have rocket club and after you make you first rocket you can design your own. Well we just launched our rockets the other day and then to day I was wondering, what would happen if i made a two peice rocket where you have a rocket without a nose cone attached to another (both with engines) with the nose cone just not glued just attached enough to where it can stay together for a while. so my question is if i launched a rocket like that would the secondary charge of the first engine give enough energy to detach itself from the top and igniting the other engine in the other rocket... Just for more information just incase you cant understand the image im trying to get at very well the bottom rocket would be attached but not glued to the top rockets fins? But would this work?