Other mistake: Lara pulls herself up to the last step twice as she boards the boat. (00:04:15)
Other mistake: When the submarine surfaces from beneath Lara, from the submarine's angle it looks like the sub is just coming up and will then level out. But we can see the submarine stays at this angle. And in the next shot we can see Lara resting towards the aft rudder. If the submarine would rise at such an angle with the aft rudder just surfacing, basically the complete submarine would be almost out of the water. This angle and Lara's position would only be possible, if she came to rest at the front side of the sub's sail.
Answer: Very plausible. The suits exist - they are called glide suits or wingsuits and lots more info can be found with a quick Google search.
Guy