I've just tried this, and I managed to get within 600 m of the station. First of all, I brought up the scenario editor and went to my ship's state vectors. Leaving the positions exactly the same, I foolishly reversed the signs of the speed, in every direction. And guess what: it somehow worked! I found myself flying away from the ISS at 14 km/s.
Then I just waited (time accelerated) until I was on the other side of the orbit. Now, even at 0.1x time acceleration, things are way too fast. So I used
Cheat Engine, which, as its name suggests, is a program that helps you cheat in games. It has a speedhack function, which was probably made to speed up the game to farm money or something like that. Well, it can also slow things down. I slowed Orbiter to 1/1000x, which means that the 14 km/s I was travelling at relative to the ISS became an apparent 14 m/s, enough to leisurely watch the station flying by.
(I didn't manage to see it however. I was on the dark side of the orbit. So I'll try again, removing all celestial bodies apart from the Earth)