Does studying architectural engineering include getting involved with other engineering courses?

Although I have a very small to none amount of expertise in the Architectural area, I am aware of other engineering curriculum. In most engineering curricula, many classes come from different engineering disciplines. Statics can come from Civil Engineering, Dynamics can come from Mechanical, Programming can come from Computer Engineering, Drafting and AutoCAD can come from Architectural Engineering, etc.

In essence, every engineering discipline will have at least something to do with other disciplines. And to be honest, this is a good thing. Many people in the industry are experts in their field but have no knowledge (not even a working understanding of fundamental concepts) of anything from another engineering discipline. This limits their ability to see the big picture. That is why nowadays employers look for people who are "all rounded", "with multidisciplinary education", etc. So I believe that if you have to wet your feet by taking other engineering courses in college, then it's for the best.

Yes, but there's a limit. As your education progresses in any major your courses become increasingly more specific to your major. Engineering is based on applied math and physics, so you would be taking those courses with other engineering majors. Now for a more engineering specific course example: architects concern themselves with the structural integrity of anything they build, that course would be called statics and you would most likely be taking it with mechanical engineering and aerospace students, but that's just because it would be a course that is relevant to your major.