While I won't disagree with any of the technical points made by the others here who are for the most part far more competent than I, I'm going to go in a bit of a different direction. While yes, an acoustic ensemble would be more practical in that space, is the youth group actually going to enjoy it? "High energy" and "acoustic set" rarely seem to exist simultaneously. (Personally, I rather dislike contemporary acoustic worship music - if I can't a loud band, bring the choir and pipe organ/orchestra back!) Rather, I think you should possibly go in the direction of some bar bands, or the youth bands I saw when I was a teen, which is to use the guitar and bass amplifiers along with the acoustic drums to fill the room and only rely on the house sound system for vocals. Yes, it's a potential for disaster when dealing with undisciplined youth, but if the musicians are able to take just a bit of direction on how to control their volume and blend with each other, it can actually work quite well. One key is to use smaller amps and smaller drum kits. The other key is finding musicians who understand their purpose is to serve congregation they are playing for and not themselves. If it can't be done, then yes, go acoustic.
As for electronic drums, my advice would be to avoid them in your case. If you don't have a near-perfect sound system, they will simply sound bad no matter what setting, and unless you use in-ear monitors, you have the potential to create the same amount of stage volume as acoustic kit - only with the sound going in the wrong direction. I ran sound for a church college & young professionals service a few years ago and the stage volume actually decreased and cleaned up a lot when we switched to acoustic drum kit thanks to it no longer being part of the monitor mix. IMO, electronic drums are severely overrated. If you need less volume use "cool-rods", brushes, or hand drums.