The theory behind how HyperDB and such plugins work is that they use a simple calculation on the blog number to allocate a DB for it at creation time, and access it later. I am not sure what exactly happens when you need do add a new DB server, you will either need to look at the code or ask for support from the author…. looking at the code seems like to can associate blogs with groups which I assume can be associated with specific servers but you probably don’t want to use this functionality unless you need it (move a very active blog).
As for the number of DBs needed, It depends very much on the load they are going to have, but your estimate of having a 33 sites per DB sounds to me as too conservative. I ran a multisite as big (30+ blogs) on a relatively low level VPS and had no performance problems with it. In the end it will depend on usage and caching, but I think you can get to 100 blogs per DB with proper caching being applied (memcache probably). Anyway the nice thing about having DB servers is that it is easy to upgrade a specific one if it gets hammered more than the others.