In a world I want to make, sailors would travel at sea for many years, perhaps up to ten, on sail boats. Obviously, they'd normally be stricken by scurvy and such, but I was thinking of some kind of "super food" that could sustain them, even if just barely. I imagined a marine plant that could suck up plentiful water, but filter out the salt and other impurities. This plant would have all the things the sailors could not fish for, especially vitamin C to prevent scurvy. And, on top of that, the plant would have a good deal of water within, so that they'd continually have a source of fresh water. Is this possible in any way? Or is this a stupid "plot convenience" concept? Thanks.
What you're describing is not a stupid plot convenience at all and there is already some GM research attempting to make existing crop plants more salt tolerant by crossing them with plants like mangrove trees and seaweed that have different strategies for either resisting salt intake through acidic roots, or methods to excrete it like mangrove trees to. This is becoming an increasingly important field of research due to soil salinity being on the increase in certain parts of the world. Crops that can grow in soils that contain more salt may well be the answer to this particular environmental issue.
The problem is, to date there has been minimal progress on this in terms of breeding salt resistant plants that contain all the nutritional value that a normal food crop plant or tree may provide. It's not to say it can't be done, but just that we haven't done it to date.
The bigger issue you face in this situation is that the tree that produces such nutritional food as you describe still needs to pull nutrients from its soil (or if grown hydroponically, from the flow of water over its roots). In other words, you can't just keep a bed of soil on a ship for 50 years and expect it to keep growing good crops. Crop rotation will help to some degree, but you will still need to replenish and refresh your garden soil from time to time. That said, your ship does actually have a source of fertiliser that can extend the life of the soil for an extended period; the sailors.
Hiding behind the pleasant name of Night Soil, human excrement has been used throughout history to fertilise crop lands and soils and actually makes sense as a source of nutrients that the plants can use to create new food. There is a catch however; human waste contains pathogens (diseases) that humans can readily pick up. In other words, you use the human waste from someone who is sick in your crops and everyone in the group is bound to get the same disease. Arguably you'd need some good antibiotics (preferably naturally occurring in the food), but in theory it's doable. Just not with plants we have today.
In short though, there are already plants that grow and thrive in salt water including seaweed, which is itself a good source of nutrition for humans, and mangrove trees which if their salt traits were bred into some form of orchard tree, particularly a citrus tree, could solve a lot of your problems. It could be watered with salt water, and then the fruit eaten in turn to provide nutrition to your sailors. Ideally, your orchard trees would use the same salt secretion method so the salt could be properly disposed of rather than a steady accumulation building up to toxic levels in the soil.
Obviously, they'd normally be stricken by scurvy and such
They don't need to be so.
Letting aside the requirement about fresh water content, certain (not so rare) species of seaweed contain all the C vitamin a human needs (see section 2.4) - even vikings knew them. A combination of seaweeds could cover all the vitamins.