ESPN.com has done a series on DIII athletic programs. This part of the series focuses on schools that have one successful DI program that benefits the other DIII sports in the program and the school as a whole.
The article points to the value of such a configuration within the athletic department and there are definitely good things to be said for running one or two big programs. You're only a little bit into the craziness of big-time programs; a little less influenced by alumni dollars; a little less likely to compromise the welfare of your student-athletes and the reputation of your school for the sake of a win.
But some of the bonuses the article cites include greater diversity because the larger programs will recruit across the nation and sometimes in foreign countries. What is meant by diversity is ambiguous. If your big program is hockey your foreign recruits are most likely Canadians and sometimes Scandinavians. These players bring a certain amount of cultural diversity but they all were raised in the Western world. Second, how much these players actually interact with the general student body is also debatable. Student-athletes can lead pretty sheltered lives.
The article also mentions a DIII school with a DI program, like Johns Hopkins, can draw players because of their academic reputations. I think this is true for the non-DI programs (so anything but lacrosse at JHU). But, and I am trying to avoid reifying the dumb jock stereotype, but I don't think it is any secret that schools with very high academic standards will lower them for key athletes they want in their major program(s). I am not necessarily suggesting this is inherently evil. But I wonder how this affects the overall dynamic within the school. A hockey player I knew who went to Yale noted that the athletes did not socialize with non-athletes.
On the other hand, a successful program can bring a campus community together. I imagine that at Clarkson where hockey rules, and JHU where the lacrosse team is a perennial success, that games themselves become social events in themselves.