FAQ for
Star Trek: The Wrath of Khan (1982) More at IMDbPro »

According to writer/director Nicholas Meyer, no. He kept himself in remarkable shape for his age, and so his costume was designed to show that off.

See also the Goofs section. Ensign Chekov made his first appearance as a bridge officer in Star Trek: The Original Series in season 2, while Space Seed was a season 1 episode. But even though Chekov was absent in the first season, he could have easily been stationed elsewhere on the ship in another rank, and met Khan in an encounter not seen in the episode. No reference was made that Chekov served on another ship prior to season 2.

Walter Koenig, who played Chekov, always jokingly suggested that Checkov kept Khan waiting at a toilet once, which would explain why Khan recognized him so quickly.