I'm of the mind that people just weren't paying much attention to stardates. As it has been pointed out many times before, these episodes were meant to be watched once or twice, then forgotten. They were put into the episodes to make the show sound futuristic, to keep the series from being grounded in a particular century, and to point up the fact that actual dates are meaningless in a spaceship traveling faster than light and carrying people from other planets. This doesn't mean they were careless, or decided to screw with people, or show that stardates can moves in any direction. It's just that they weren't important, unless they were factored into a story, like those with "no stardate" or "stardate unknown" or something. Look at James R. Kirk's tombstone with his birth stardate. Makes no real sense.
Was Chekov on the ship during Space Seed? No, not if you think in real world terms. The character wasn't created at the time. However, if you think of Star Trek as its own "reality" then why not? He certainly could have been. Do you accept Marla McGivers was on the ship during episodes filmed before Space Seed? Or Lt. Spinelli? Or did they only join the ship just prior to the events depicted? If there was a line of dialog in TWOK which said Chekov was down in security or something when Khan was found, you'd probably buy it then, and all that would be is a line of dialog written by someone 15 years later. But in the Star Trek universe, it would be a concrete fact instead of fan supposition.
The way I see it, unless a character is specifically introduced, then there's no way to tell how long we're supposed to believe he/she has been on board. While Walter Koenig joined the cast in Catspaw, Chekov was assigned duty on Enterprise sometime after Mudd's Women. That's all we know.
