#Yes
Would a single planet benefit from supersonic submarine trains to go from continent to continent.
##When the Cost-Benefit of supersonic submarines exceeds that of starships, it'll benefit the planet to use supersonic submarines. Specifically, when the cost of using starships to transfer goods between colonies, stations, and other points of interest on a given planet exceeds that of using supersonic submarines, the latter becomes the cost-effective solution.
Where would we see this?
###1. Ocean Planets. Despoina in Mass Effect (where the leviathans live), Atlantis, etc... Cost-benefits will favor submersibles when the civilization is not only spread across the ocean's surface, but also makes use of submerged colonies or stations, and/or mine resources at the bottom or beneath the ocean floor.
###2. Subocean Planets Enceladus, Naboo
This is fairly self-explanatory. This includes planets with a thick surface crust that hides a subterranean ocean or planets with large quantities of subterranean seas and oceans like that seen in Star Wars Episode I's Naboo. In such cases, spaceflight and atmospheric travel is either unfeasible or may be more costly than a direct trip through the subterranean oceans.
###3. Oceanic Planets with frequent storm activity. Kamino in Star Wars Episode 2. Oceanic planets with frequent storm activity will pose a problem to starships and atmospheric flight in general. While small storms may not be an issue, particularly larger storms such as Hurricanes, Monsoons, Tropical Storms, or super-storms as we've seen in films like The Day After Tomorrow, or in Stargate Atlantis' The Storm will present logistical or physical obstacles. For civilizations such as Star Trek and Star Wars where spaceflight is cheap and powerful employing high technologies such as deflector shielding and/or antigravity, this can be limited to eliminated. For galaxy-spanning civilizations without such robust technology (such as Mass Effect) this will not be the case. In that case, development and use of supersonic submarines would be of some or great interest to inhabitants. This would be proportional to the severity of the storms experienced, be it tidal waves that disrupt landing platforms, electrical activity in the upper atmosphere (lighting releases X-rays for example), wind speeds that make air-travel difficult, or air-pressures that make flight impossible (Day After Tomorrow).
###4. Planets that otherwise disrupt starship activity. Miller's Planet in Interstellar. The gravitational tidal waves from the nearby blackhole are extremely powerful and are liable to destroy starships entering or leaving orbit that do not take care. Additionally, the time dilation effects of going in and out of the atmopshere would pose issues to inhabitants on the surface.
Oceanic planets with an atmosphere similar to Venus, or a magnetosphere similar to Jupiter would also disrupt space travel extraordinarily. Typically, it may become cost effective to limit trans-atmospheric flight in favor of ground and water transportation. If the planet is also of an oceanic type, then water and submersible becomes far more effective.
#No ##When the Cost-Benefit of starships exceeds that of supersonic submarines Specifically, when the cost of using supersonic submarines to transfer goods between colonies, stations, and other points of interest on a given planet exceeds that of using starships, the latter becomes the cost-effective solution.
Where would we see this? Typically on worlds where starship travel is not disrupted. More importantly, this becomes much more present in galactic economies where starship travel is cheap. As we saw on Kamino (Star Wars Episode II), that is the case; but, as we see in Stargate Atlantis or Mass Effect, that is not always the case for civilizations that encompass a galaxy. A galaxy wide civilization with starships. Supercavitation makes them faster than planes, but would a starship just be easier?
Note: I'll provide more links to examples later today.