Not in the US Navy. Part of the reason the US Navy standardized on PWR is that while it's not the most efficient it is something you can restart at depth if necessary. The lesson of how much that matters was driven home by the loss of the USS Thresher.
It should be technically feasible to restart a liquid-metal cooled reactor at depth just as easily as a PWR, especially a Na- or NaK-cooled one. Certainly keeping the coolant liquid after shutdown can be a challenge but as long as the plant has operated for a while there should be significant decay heat to keep it warm, and trace heating in the pipes could be powered by auxiliary power if necessary.
The kind of emergency restart procedure employed today would work just fine on a MSR design. We're talking restarts on the order 1-10 minutes after an emergency shutdown. That's not nearly enough time to solidify the core, even when you are drawing some steam for emergency propulsion needs while the reactor is shutdown.
