No. Let's start with the fact that people will die out from solar radiation, long before they move away from their home planet. Protection against this exists only in theory. Well, the cycle of substances on such a ship exists so far only in fantastic books.
Everything depends on money, if humanity had a task - to break into a cake, but create a colony on Mars, then in five years we would warm up the motors on spacecraft to the Red Planet. The same is with the expedition to Proxima Centauri. Give me two or three trillion dollars (the annual world military budget) and in fifty years such a ship will be ready. I think it will be a disk 10 km in diameter. and 1 mm thick made of carbon fibers (weight 20 thousand tons - like an average sea vessel), which, while rotating, catches hydrogen atoms in space, throws them to the periphery, where an annular trough collects hydrogen and pumps it into the center, from where balls (with a diameter 1 cm) of deuterium (this is 2% of hydrogen), which, falling into the focus of laser beams behind the ship, create a mini-thermonuclear explosion. An explosion every second. Craving appears. According to my estimates, a day at a speed of 30 thousand km. per second you can get 2kg of deuterium. This is 73 tons in a hundred years. Plus our own reserves from Earth - 1000 tons of deuterium, 100 tons of tritium, and 1000 tons of uranium (for the operation of a uranium reactor - as a starter, and - as a backup option - for reliability) The supply and replenishment of fuel must be tenfold, so that the descendants of the first space pilots could return to Earth, because it is not known what awaits us, and whether the colonists will find a suitable planet for settling .. To make such an apparatus in space will be half an order of magnitude cheaper than on Earth (excluding the delivery of materials by an electric gun to high orbit). The absence of air and (conditionally) gravity, low temperatures will allow a thermonuclear reaction under simpler conditions, use superconductivity and build an apparatus of any size with minimum strength .. This disk is also complex like a Fresnel lens and is a pseudo-parabolic antenna for communication with the Earth. The central part of the ship is a thin needle with a diameter of 5 meters and a length of 10 kilometers (to reduce the midsection and the likelihood of collisions with macro-bodies) The disk, alas, will perforate with such macro-bodies (although this is unlikely) and be repaired along the way. At the end of the needle (like Koshchei's) there will be a living block, protected by the thickness of the needle's body from explosion products. In this needle you need to somehow shove all the equipment and people. Each milligram of mass counts, so it is better not to drag so much meat over the distant lands (which requires thousands of tons of food, provision and protection) There will be space pilots (and I am among them) who will agree to fly as a stump - without legs, arms, spleen and other unnecessary liver and failure. It is enough to leave the brain (without a skull), eyes, inner ear, kidney (one), a piece of liver, all sorts of glands, stem cells for the treatment and restoration of the body (in a colony on the planet) ..., and - everything (for everything everything - 8 kilograms, and food -50 grams per day directly into the blood, like oxygen). Why do I need a body on a ship if I can perform any operation with robotic exoskeletons? And with me, of course, I will take millions of yaycells from which normal babies are born, and all sorts of animals and plants to create a colony .. The front part of the disk is a "prerabolic" mirror of a radio telescope, which probes space in search of islands for settlement, or "infection" with life. Pilots (full-fledged individuals, enclosed in capsules with a brain) will not get bored, they will have a hectic creative life, interesting work, communication, personal life, personal space, property, business, rights, their own destiny, weddings, divorces, intrigues, hobbies, friends, discoveries, disappointments Holograms controlled by a real brain will communicate, which is already available ... If suspended animation is not yet available, these organisms can live in a ship in controlled half-sleep, when a year is perceived as a month, and the organism itself will be very slow to grow old, being in ideal conditions and easily survive a hundred years, being at this age in the state of a thirty-year-old person who has lived in a city with a dirty environment, beer and stress. Pilots will have to improve the rapidly obsolete ship according to instructions from the Earth, send probe boats to celestial bodies, so there will be enough work .. The ship, of course, will become very outdated already at the moment of launch, but such is the logic of progress. In twenty years, a new ship will catch up with it and transfer the pilots to itself, and the old one will be scrapped. In a hundred years of acceleration, movement with the engine off and braking, you can reach the nearest star. But few people on Earth need it now.
Literary and cinematic fiction marches triumphantly through books, films and the minds of dreamers. :)
Modern technologies allow to have a colony of 10 people at an altitude of 337-430 km above the Earth's surface, which requires regular supply of consumables and tools.