I have a netbook right now (and I like it!) and I also had the same idea as you: have a netbook for mobile use but have a nice desktop at home for most of my work. The more I thought about it though, the less I thought that this arrangement is a good idea. Here are couple of reasons,
1. One is the right number of computers in your life. Trust me on this issue, and even if you don't, trust Randy Pausch who also said the same thing. At one point, I had five computers in my life, and while this polygamous arrangement was necessary at that time, managing data consistency over so many computers was hell. Simplify your life, try to stick with one computer. Back up your data often but you really want to stick with just one computer if possible.
2. Netbooks are portable and great, but they are not for long sessions of work. The small keyboard and screen are fine for short sessions but any long sessions (more than 30 mins IMO) of work, it becomes a hassle. I bought a small keyboard that I carry around when I know I'll be using my netbook to take notes or minutes to avoid this problem. There's nothing I can do about the small screen though. My netbook is basically used as a PMP and e-mail-on-the-go machine. I don't really use it for document work unless I have no other choice.
The issue of not having an optical (DVD or CD) drive is really not that big of a deal. Flash memory is so cheap and convenient that you really can get away without having one. In fact the laptop I intend to purchase (Lenovo X200s) will not have one either. I carry around a 4 GB (and will be getting a 16 GB one soon) flash drive with me, so if I need to install anything off a DVD, I copy the contents to this flash drive and run it off of that.
To give a direct answer to your questions.
1) I think a laptop or portable computer is absolutely necessary for b-school. You won't just be working on individual assignments, you will be working in teams a lot that means you need to have some form of a portable computer.
2) I think a netbook + desktop solution is also doable (you're probably not going to be running any hardcore simulation software when you hold your team meetings, so you can do that stuff on your desktop) but I think a single laptop solution is much more convenient and sensible.