I started playing on the site almost a year ago. I have played in three OTB tournaments since, and gained 125 points total from them.
(Disclosure: My OTB rating has fluctuated over the years, so I have merely moved back to my former peak rating- but I think RHP is responsible).
I have used RHP for two things to help my OTB:
1. I use it as a testbed for new ideas, especially in the opening. I've played all sorts of interesting stuff that I wouldn't necessarily play in OTB-but now I might, as I have logged lots of experience and plenty of practice.
2. I use it to refine my technique, especially in the ending. It's one thing to study endgame books generally, but it's a whole new ball game when you have a specific position in front of you, and you can pull out your endgame books to study and figure out the best plan.
3. It was unanticipated for me, but the forum has been valuable. I am exposed to a great many different opinions, and I think it is valuable to have your opinions and assumptions challenged by other players. You will gain new insights into the game, and learn valuable lessons by association, rather than in a game you lost.
The biggest mistake I have made is to let my game volume get too high. The quality suffers, as you lack the time to crunch them all.
Edit: to answer the first question- when I have fewer games, my RHP rating exceeds my OTB rating, but when I add games and start playing here like it's OTB, my rating falls to the level of my OTB rating.