As regards transmitter power - there is a legal limit on power for model use - I dont know of any hobby grade TX that transmits noticeably below this. Obviously, none transmit above that power. The toy grade ones (the ones that come in set that costs less than a decent set of batteries) usually run off a PP3 and have a bit of bent wire for an aerial, and have a range beyond arms reach, but not much. Range, for hobby grade, is more a question of line of sight, the quality of the receiver and siting of the aerial, as a rule of thumb, the higher the better.
2.4GHz signals tend to bounce off water much more readily than lower frequencies, and are very line of sight. Salt water tends to absorb any signals very readily, thats why transmissions to real submarines happen on very low frequencies, and to receive them the sub has to trail about a mile of wire and be very near the surface. Model ones work great in fresh water, but lose signal very close to the surface. At least, the ones that I have seen do.
In most boats running on calm water signal pick up is no problem, the small aerials are easy to hide and still work fully effectively. On 27 I have "controlled" at yacht at 400 yards. On 2.4 the furthest I have done is about 200 yards, but that was a 3 foot long warship painted in camo, so any further and just seeing which way it was pointing would have been a problem.
When the aerial vanishes down a trough between waves, signal will be lost. Just how long it takes for the signal to be re-established and what the controls do in the meantime is a matter of guesswork. In the linked vid, there appeared to be a long whip aerial, indicating a lower frequency setup. This is much more likely, in the conditions shown, to get a usable signal for more of the time.
