IIRC, explaining that Chekov was off getting retraining in Security dates as far back as his character's absence in TAS, and Koenig being fitted for a red uniform for "Phase II".
Also, some fans feel he was working security at the time of Space Seed to accound for why Khan recognized him.
Considering the TOS Enterprise had a crew of 430+, he could have been a member of the crew doing one of any number of things during the events of
Space Seed, not necessarily security.
Given that fact that he implied in TWoK that he WAS part of the crew back then in some unspecified capacity, I have no reason to doubt that he was one of the 430 crew members in
Space Seed.