I like your motivation for this feature request; private betas definitely do better when the people who had committed to the proposal remember their commitment and are active on the site often in the early days.
That being said, I don't agree that auto-sorting private beta sites to the top of the list is the right solution. Since the primary purpose of the site switcher is navigation, it seems a bit strange to have the system make a change that is inherently ephemeral. (Sites are generally only in private beta for a week or two.) Having the order change in the matter of a few days, without the user actively deciding anything, seems like it might do a little more harm than good. I suspect a lot of people would file bug reports asking why X site disappeared from their list when it was just there yesterday.
Animuson pointed out that there's an outstanding feature request to allow users to customize the sites that appear at the top of the list. I think this solution solves your problem nicely, though it requires an active decision on the user's part. It does require that a user join the private beta, then remember to move the site to the top of the list, but it's a one-time action that will provide a reminder to them to visit the site every time they're in the site switcher.
I'm not going to decline this request outright just yet in case someone else comes along and makes a compelling case for this, but in my opinion, this problem will be mostly solved soon when we allow customization in the site switcher.