Yes, that's pretty much it. I think in St. Ralph he doesn't actually win, but takes second, which back in the 50s would be in the 2:20s. Heck the race was won in 2:31 in 1952.
The movie itself is about miracles. The themes and messages wouldn't work if the movie were about a runner achieving something expected, ordinary, and well short of miraculous. It only works if the attempt is nothing short of being a miracle. The story exists in the universe where miracles do happen, including the mother waking up from the coma upon receiving the silver medal. Through the catholic teachings in the film, Ralph is taught what it takes for a miracle to occur. So we have two miracles occur in the movie, through means explained by the movie itself. Miracles happen in the reality of the St. Ralph story, that's a fact of the story's reality. The question for the viewer is, how can miracles be achieved in our own reality, in our own lives? Each viewer will probably have very different answers to that question. Some may feel more connected to the spirituality aspect, some more connected to the hard work. I think for all the message of St. Ralph is that miracles aren't going to happen on their own, but through your own actions/prayers/etc.
If you are just watching St. Ralph for the training and racing aspects and feel the realism is a problem, then you are missing the entire point of the movie.