I think it can... Here is what happened to me.
I started today with a wonderful thought. I had completed all my research items! So I sent my normal 9 attacks to lvl 5 NPCs around me.

While they were attacking, I thought hmm, I have all the tech I need, I no longer need this Academy, and I can replace this with another Barracks! Yay me!

So I used up my first Dynamite, and destroyed it. I then proceeded to start building my barracks.

Well, my attacks started, and I was very surprised that nothing was returning at all! I looked at my reports and saw, yep, every attack defeated. Lost 4500 ballistas and transports today, all because I demolished a building. So, if you dont have an academy, you dont have any tech. Hard lesson learned.

Rae