We heard the figure 430 a few times, but Captain Pike had a crew of half of that, with the same basic ship.
In Journey to Babel, they took on 114 delegates (of whom 32 were ambassadors), Sarek came aboard with 2 aids and a wife. If 1 delegate plus 3 others was typical then the number of people aboard the Enterprise would have been nearly a thousand. Although I've consider the possibility that they might have remove the science contingent for that mission. Even still, the ship would have been stuffed.