In my experience: you typical undergrad will as an undergrad have pretty much nothing in the way of interaction with the professional schools, and your professional school students will later have not all that much interaction with the undergrads; a little more mixing between undergrads and graduate students, but not all that much.

What does happen is that later on substantial #s of your classmates while wind up having having gone back to the law school or the b-school or whatnot.

This means that even if you, personally, never met anyone at the b-school, you probably know people who went there later on, making most b-school people only a couple degrees of separation away from you.

This means the big alumni network is loosely connected, but is comparatively connected, and predictably so; it's also the case that probably someone in your undergraduate class went to Wharton (or whatever) and thus probably there's some chain-of-acquaintances connecting you to the class at Wharton some year, but it's a lot more tenuous than the intra-university network.

So, short version: not that much interaction @ the time of study; across time, the alumni bodies are much more cross-linked (though admittedly not to the same extent that you see inside the particular sub-schools).