Very interesting, but not practical.
Many pellet guns operate in a rage of approximate 390-450 Feet per second velocity at one atmosphere. Some higher I guess, but that is the figure on the guns I checked. I am certain some math wiz could come up with a quick formula that would give the velocity at 2 ATA etc.
But in the end, the analogy with the pistol bullet penetrating only 6 feet of water is probably more relevant. The 9mm pistol is operating at a velocity of 1080-1250 Feet per second (according to my reloading manuals) with a heavier projectile and more surface area. So given that the 9mm had a velocity of roughly 4 times that of the pellet pistol, it would seem reasonable to expect the pellet, with its reduced mass and surface area factored in to go maybe 2.5 feet or less. Greater depth may also affect the velocity.
Then we have to factor in the pressure of the CO2 cartridge. I could not find any information on this, but would imagine it is in the lower end of the spectrum (guessing 50-100 PSI keeping in mind many pellet rifles are hand pump versions so the pressure cant be too high). Again someone with more time and brains than I could quickly look up the depth at which the ambient pressure would exceed that of the pellet pistols CO2 cartridge. If the pressure of the CO2 is 100 PSI then I bet you would not have to go that deep for it to not work at all.
As for the sling shot, estimated range 1 foot or less and then it would not do much if any damage.
But the above would be a fun experiment to observe.