No, the Cougar is nothing to do with missions (in the 6502 versions, anyway - the other platforms have different mission code). It's just a rarely called part of the random spawning routine. Very rarely called.

The mission-related ship is the Constrictor, which you only bump into at the end of that mission.

Obligatory link: https://elite.bbcelite.com/deep_dives/the_constrictor_missio...