Yes, they will overlap. Simple example - draw out your building floorplan, and the approximate locations of the existing AP's. Now draw circles around them. BUT...you have only 3 colors to draw with (corresponding to channels 1, 6, and 11). You'll have a tough time doing that where 2 adjacent circles aren't the same color (channel). Adding more AP's (of any kind) on top of that is just more circles, same colors..so now it's even harder. Extra credit for adding more floors...
The colors correspond to available spectrum.