No, they can't
I haven't seen an entry in any official publication that describes water, specifically, as something vampires can or cannot consume. But we have quite a few examples suggesting that they can't:
Even the Eat Food merit doesn't let you do anything normal with the mortal sustenance you consume; it sits in your stomach until you vomit it back out later. You just have an easy time holding on to it until it's convenient to expel:
Of course, you can’t digest
what you eat, and there will be some point during the
evening when you have to heave it back up. (V20 Core Rulebook, page 480)
Fifteenth generation and weaker vampires have some better-than-normal ability to consume mortal foods, but they too are unable to keep down food or drink:
You can hold down mortal food and drink
for an hour or so; other vampires vomit immediately if
they try (unless they have the Eat Food Merit). (V20 Core Rulebook, page 481)
One power listed under Thaumaturgy causes vampires to be unable to consume blood, treating it as any mortal food or drink:
The victim of this power can no longer consume
blood, vomiting it up as he would mortal food or
drink. (V20 Core Rulebook, page 227)
The Nagaraja clan weakness requires them to consume flesh as well as blood to survive, but this line explains that that weakness does not give the Eat Food merit. It explicitly states that the vampire cannot drink non-blood liquids, generally:
does not allow them to eat food or consume other
liquids. (V20 Core Rulebook, page 407)
The game doesn't really simulate this too closely, but it's also worth noting that most water a vampire might encounter (especially in the ocean) isn't going to be just pure water. It will have things dissolved in it which are certainly not water, and those will be problematic. They cause problems even when added directly to blood! Consider the Necromancy ritual Minestra di Morte:
The necromancer obtains a piece of a dead body and
simmers it in a pot with half a quart (or half a liter)
of vampiric vitae. To this stew, the necromancer adds
rosemary (for remembrance), basil (the funerary herb),
and salt (the alchemic principle of clarification). After
bringing the concoction to a full boil, the necromancer
eats it. [...]
Necromantic vampires without the Eat Food Merit
(see p. 480) can’t keep the soup down, but can still use
the ritual and gain the information. (V20 Core Rulebook, page 178)
Some flakes of herbs and a pinch of salt, coupled with some simmered meat, makes the blood indigestible. Even if pure water were OK for vampires to consume, most of what they encounter won't qualify.
If not, how does that interact with swimming, or falling into water, and accidentally getting water in their mouths?
I don't think that these would interact. Getting water into your mouth doesn't mean you need to inhale or swallow it, and when that does happen it tends to be down to issues around trying to take a breath. Vampires have no need to breathe and so there is generally no reason for them to even open their mouths while in the water, let alone swallow some of it. By that token, most humans have trouble swallowing seawater, but that doesn't preclude swimming or coastal living.
Vampires don't have any physical processes related to eating, digesting, or passing material through their intestines, and all mentions of their consuming anything other than blood (Nagaraja excepted, plus a couple of odd Disciplines) describe the need to vomit it back up later. Nothing comes out the other end, so to speak, and there are no digestive operations that move the water out of the stomach or absorb it or do anything at all with it. Generally speaking, they can't consume any material other than blood.