Ok there are two ship in water sequences, the first is rising out of the water. the second showing a ship crashing in the water is not the same ship, the nacelles are further apart and smaller in proportion to the saucer.
The first looks like the JJ Enterprise the second looks like a prime universe Constitution refit.
Refit engines are not rectangular, they are cylindrical with a rectangular bussard ramscoop and a bladed tail section.
A ship crashing into the water, ok that's conceivable, it plowing a huge wave in front of it and not breaking up on impact, not so much and a ship rising up out of the water intact goes directly from incredible to ludicrous. The whole point of these ships having shuttles and transporters was because they were too big to land. Space craft are designed to survive vacuum not crushing pressure, impulse engines are atomic fusion powered, use in atmosphere isn't possible, one for environmental reasons, but more importantly because the engine would consume itself and damage the ship propelled by it.
This is Star Trek, not Space Battleship Yamato. Sure this is sci fi so anything is possible but even so in Trek there have always been reasonable limitations on what ships can do.
The Enterprise D force landed on a planet and was rendered unsalvageable, the JJ Enterprise which is the same size though technologically 100 years less advanced, can not only enter an atmosphere, it can submerge and take off again intact.
I will watch the movie and I will probably enjoy it, I do like science fiction and action, but I'm not going to think of this as a Star Trek film, the apple has fallen way too far from the tree.
Let's not judge it till we've seen it. For all we know there's a perfectly rational explanation that comes up in the film.
"It's not safe out here. It's wondrous, with treasures to satiate desires both subtle and gross. But it's not for the timid."
If you control the rate of decent by various technobabble means (reduced mass via subspace fields, anti-gravity, landing thrusters... Voyager-babble) you put the ship down in shallow water and touch bottom.
The hull is sealed to prevent air from getting out, no water can get IN so long as all hull-ports are sealed. I would assume they have something similar to "condition zebra" for sealing openings and such.
So you touch down in the water, you keep your SIF energized (which keeps the ship from crumpling under massive acceleration, 1G of gravity and water pressure is nothing) and submerge until the ship touches bottom... You now have the benefits of all that water supporting your ship without the need for bad Voyager-esque landing legs or technobabble excuses.
Takeoff, would be a slow accent giving time to allow the water to drain from large flat surfaces.
It's totally do-able in terms of canon-technobabble and basic logical understanding of engineering.
Weather or not it's "Trek" is up to you... Consider this though: I subscribe to the "canon is defined by what we see on screen" school of thought. We now have starships in the water, therefore it is canon. Argue all you want you WILL NOT change my mind.
ISE ISE Ba-bee. "If you got the Borg yo... I'll solve 'em check out this shot while my torpedos dissolve 'em"