Sometimes they do. But saracens are faster than harvesters, so always can run away. When the distance to the harvester has become large enough, they give up (as for any UFO chasing a faster ship). By repeatedly holding position and moving, the harvester can be lured into ground defenses range.
Re on the sparrowhawk exploit. I think a similar technique should be usable on starchaser vs gunboat. A gunboat has 3 particle beams in addition to 2 alien launchers. A starchaser can only be equipped with the 2 launchers, but she's faster than gunboats and by staying out of range of the particle beams, the weaponry can be made equal. Hitpoints and electronics are superior, so a won fight.