Okay, first off, to answer the question of how he would have survived, we need to consider what are the leading possible causes of mortality in falls from waterfalls.
First: the freezing cold water. Though the temperature shock can cause cardiac arrest on impact, this is not an enormous concern for someone who is fairly young and without an underlying heart condition. Since (as per the dates on the gravestone) Holmes was 37, and certainly someone who led an active lifestyle, we can safely assume his heart could indeed take the strain.
The other and more prevalent danger is the human Cold-Shock Reflex, which causes hyperventilation (and immediate gasping of course) in response to the temperature change.
Gasping in water is the obvious danger. Hyperventilation is the more insidious one, robbing the body of oxygen that it desperately needs, and causing exhaustion quickly.
In any case. Cold-shock reflex is the number one killer out there for any kind of plunge into cold water, but is entirely preventable so long as one remembers to suppress the reflex. Not easy but perfectly feasible, so long as you're not too busy panicking. Holmes definitely wasn't.
Of course we've all heard of hypothermia, but it does not set in as quickly as might be imagined. The US Marine Corps gives about 15 minutes for hypothermia to set in, on average, in freezing water, and though with an already serious injury, Holmes would not have been on the high end of that scale, again, getting out of the water in that time is possible.
Second: Post-impact conditions.
Unlike when one hits standing water from a great height (which is about as bad as hitting concrete) water near the base of a waterfall is thoroughly whipped with air and so provides a comparatively soft landing. The good news is that one does not get killed by the impact with the surface. The bad news is that it is impossible to float (and near impossible to swim) in this kind of water, and once submerged, even in the presence of daylight it is pitch-black because of the light blocking properties of the microscopic air bubbles. Adding to this the fact that the currents -and the impact- rob a person of any sense of direction, it is usually impossible to break surface before drowning, and worse, attempting to do so either does nothing measurable, or brings a swimmer back into danger as the surface currents tend to flow towards the falls.
If a person however knows their physics (Holmes did), can stay calm long enough to regain orientation (he did have a pretty cool head after all), can manage not to drown while attempting to do so (hence the usefulness of the oxygen device), then it is possible to get carried away from the waterfall by swimming diagonally DOWNWARD and away from the fall, where eventually one hits a deeper (and always outbound) current.
Third: Impact.
Okay, so now we know that the impact with the frothy water is not so bad, but what about rocks?
The greatest danger is right beneath the falls (because of rocks that get washed over and go straight down) and if anyone noticed, when Holmes did break away from Moriarty, he used the momentum to push away from the base of the falls. Pure luck? Possibly. More likely, though his eyes were closed, he was probably keeping track of their relative positions thought orientational perception, and broke away at the optimal time to get out from right under the falls, but not far enough to hit water that would have had too little air to allow for a shot at surviving the surface impact.
So, in summary, Holmes avoided the largest danger of hitting rock, used the oxygen device to breathe underwater until he could regain his bearings, and then probably swam for a current that he could ride away from the falls, and finally surfaced, then exited the water and found some kind of shelter before freezing to death, or was found downstream.
It is possible that he used the device just before impact (so that when the cold-shock reflex was triggered, he would not have drowned), but unlikely, since the risk of losing it would have been far too great.
More likely, he took a deep breath before impact, held it, suppressing the initial gasping phase of the cold shock reflex, and then used the device underwater.
Easy to survive? Hell no!
Possible, yes, especially if you got a mind like Sherlock Holmes did which never ever shuts down, and nerves of steel.