The short answer? Well, there is no short answer, so let's get right into it I guess.
Is it possible to win with a sub-optimal Pokemon? Absolutely, even at high level tournaments (see Pachirisu in VGC). If you understand what that Pokemon can do, what it can't do, and build your team to support it, and if your opponent doesn't know what it does or how to play against it or is simply less experienced/skilled than you, you can easily win with an otherwise sub-optimal Pokemon. Hell, you can win with a team of 5 Pokemon and an empty slot if you're good enough and those 5 Pokemon form a team that covers the threats you're likely to face in your chosen format, so you could realistically fill that empty slot with whatever you want and "win" with it, even if it essentially does nothing productive in the match (there was an example of this in a pretty high-level Smogon tournament some years ago where the winner brought a Pikachu which ultimately did nothing other than get sacced to a Manaphy to get a check in safely, but I can't seem to find the replay).
The problem is consistency. While you can win with a sub-optimal Pokemon, or even a sub-optimal team, it definitely lowers your chances compared to a more viable Pokemon or team. If the Pokemon you're using is outclassed by something better (as most low-tier Pokemon are), your mathematical chances of winning with the Pokemon who outclass it are almost always going to be higher. Using these Pokemon is always going to be a handicap; you can still win despite the handicap but you'd win more consistently without it.
This is where I think a lot of more casual players don't see eye to eye with more competitive players. Competitive players often don't care about using their favorites; they'll use whatever gives them the best chance of winning. This naturally gives them an advantage over players who might insist on using their favorites regardless of viability, and while you absolutely can overcome that advantage and beat competitive players with a, for lack of a better term, "casual" team, it often requires you to be significantly more experienced or skilled than your opponent. If you take two players of an even skill level and give one a competitive team and one a less viable casual team, the player with the competitive team is going to come out on top more often than not.
This is also where you see those cookie-cutter archetypal teams that utterly lack creativity spring up. If something works very well in the current metagame and gives the user the best chance of winning, a lot of competitive players are going to pick that up and use it instead of using their own teams, or use teams that are heavily based on the principles that make that team succeed, which results in a lot of teams that are essentially the same, or certain viable Pokemon having very high usage statistics. It's an inevitable byproduct of the competitive mentality.