It seems fairly common for people to cross the A&P without meditative experience, I clearly recall experiencing this at around 11 or 12 years of age for the first time and also remember several passes through it over the years between then and beginning insight practice. I was a chronic dark nighter for years due to this, cycling through what I now recognize as the progress of insight but never knowing how to do anything about it until I found MCTB and this site. I've said before that I got stream-entry pretty much by accident too, I had no idea about vipassana and had no interest in Buddhism so I've got plenty of experience of this sort of thing "accidentally" or "suddenly" happening.

When such a person start doing meditation, what impact this is going to have on his practice compared to a non-dark-nighter?
In my experience, it was finding out that these stages had been mapped and described in detail, descriptions which fitted exactly with what I had been going through periodically for years, that made the big difference. Due to the manner in which I attained 1st path, I can't really say how this works pre-path but after that point, since cycling continues, knowing that all of this stuff is just par for the course meant that it became less of a problem to be dealt with and more like something to be investigated.
Does that person has to climb the ladder from the ground and eventually experience another A&P?
Yes, until you land 1st path you'll cycle through the ñanas repeatedly. After 1st path happens, and before the progress of insight for 2nd begins (a.k.a. Review), you cycle from A&P to Fruition and back.
Or is the person cycling in the dark night stages with very few ability to deal with it (not having the chance to learn to swim in the shallow water of stage 1-4)?
As above, you cycle from 1st to 11th until you hit Path. As also stated, I don't know about pre-1st path so I don't think my opinion would be of much use to you here.
Dark Night is about surrender, not in the sense of giving up but in the sense of equanimous acceptance of what arises. If you can learn to see how none of this stuff is actually happening to a self, even the most unpleasant and difficult of sensations, you can begin to understand why this is the case and gain insight into suffering as a whole. Observe objectively, don't wrestle with it and learn to navigate the territory skillfully as it will stand you in good stead for future progress.