Tanks do shoot their main cannon, but I believe its just random, and the accuracy gets substantially better once you have good soldiers. One of my starting riflemen has 88 rifle 100 exp and 76 morale, he hits about 75% of the time with the basic rifle and kills entire waves in a matter of seconds.
I love this game, but I keep getting a bug where one or two German soldiers slip past my soldiers and get to the end of my side and I lose, even though I haven't lost any of my lives.