What happens to active VIP/node connections if the underlying pool is changed?

Your persistence method is going to create a table entry on the F5 that maps a client source address to a node IP (and port). If you just remove that node traffic flow will simply fail. If, however, you have a good monitor applied (that can reliably detect the absence of a node) and Reselect set in the pool's "Action on service down" option, a persisted connection to a failed node should be re-loadbalanced to a new node.