There are many variables that determine the exact time of reconvergence for spanning tree. Generally speaking, any traffic that goes across multiple switches will see a brief interruption if and when spanning tree root changes. The service interruption should generally be on the order of a minute or less.
Features such a RSTP and backbone fast can help but I don't believe "zero downtime" is possible since the spanning tree algorithm, even with tuning and ideal conditions, will take some finite time to converge to the new topology. Even RSTP, under ideal conditions, will generally take a few seconds to converge.
