I mean, you can do a Gunpowder rush, but what's the point really? CR Maces are way stronger, and none of the unique Musketmen are really all that impressive. Janissaries maybe, but really? Muskets don't get City Raider promotions, so really Maces are probably gonna be just as good on offense and the bonus on defense isn't really good enough.
Musketeers? Good support unit, but you're not gonna win a war rushing with them on Immortal or Deity. You're gonna need siege, which neglects the 2 movement.
Overall, Gunpowder seems to be so weird in the tech tree that its not really gonna be worth it to beeline it. Either Engineering will be sufficient or Cuirs are called for.
Carrack rushes with Portugal seem to be a good idea, but they look better than they smell in my experience. What good are you gonna get from it? If you're gonna settle new islands, you're gonna need Astronomy. Otherwise you won't be able to profit from the new cities. Or in other words: in most any game that would make early Optics profitable, getting Astro right after Optics is gonna be the most powerful play. And in most cases you're gonna get Astro via double bulb as soon as you get Optics if you can wing it.
I don't have experience with all the UUs and beelining them but as far as I can tell, pretty much the only one that makes beelining it worthwhile would be the Praetorian. If you play the Romans and you go for IW real early, that can make it worthwhile in that sense. Of course you can rush with other UUs, but I wouldn't call it beelining for a tech if you're going for AH early with Egypt, since it's such an early tech that the term "beelining" is quite a stretch.
I have done Archerpult, I have done an Engineering bulb, but I can't say I've done anything out of the ordinary like that in order to win the game.