Snorgy,
My particular check was spring mounted. It would only chatter at specific speed/frequency range - probably related to pipe volume, flow velocity and spring rate. We swapped for a swing check, and it changed the frequency and pump speed a little, but still chattered.
A similar test stand had pumps in series also, but just motor starters (no VFDs), and yes, the downstream pump could, if not started first, have the impeller start to unwind (different pump style, and much larger pump). Upon starting, you could hear a godawful crash as the impeller tightened back up and hit its stop. This pump had a set of manual bypass valves, which (to create the problem) were sometimes not used properly by technicians, because it involved a lot of walking back and forth. (If you design something that is hard to use properly, and easy to use improperly even if that causes damage to the equipment, expect the latter to be the normal way people will use it)(even if they paid money for the equipment).
Those large series pumps were replaced some time ago by an even larger pump and VFD.