So now I finally had a real run using a Vulcan. (Didn't finish yet, had to stop at sector 7 to get to sleep, but looks to be on track for a win.) With Engi C. I still bought it way too early (sector 1!) but at least this time didn't pair it with a teleporter. 
What makes the Vulcan sing is max cloaking and hacking. Cloak for 15 seconds, wait for 10, then drain the weapons of that charge and block 10 more, which total just happens to match cloaking's cooldown so then cloak again. That gets the Vulcan to full chain before the enemy shoots at all.
But it still takes the Vulcan a while to actually drill through the shields. With any amount of enemy evasion, it barely keeps up with shield regeneration. It mostly doesn't break through for damage by itself, just keeps the shields down. It needs other weapons or drones for the actual damage. And a Defense Drone II versus a Vulcan is a hilariously spectacular fireworks show -- but effective on the part of the drone.
It's not the best weapon in the game. I'd rather have a Glaive Beam. Same deal of 4 power and a long charge and relying on other weapons for support, but deals its damage more immediately and effectively across multiple system targets. I'll see how the Vulcan does on the flagship, but I think I'd rather have a Glaive there too to whack both the missile weapon and shields together.
The Vulcan feels like overkill win-more. If you can turtle long enough to spin up the Vulcan, you can turtle long enough to win in any number of other ways, including beam weapons which do the same job faster and more reliably. It's still very good if you don't come across beams or enough shield-stripping for them, though. It's one of many solutions.

What makes the Vulcan sing is max cloaking and hacking. Cloak for 15 seconds, wait for 10, then drain the weapons of that charge and block 10 more, which total just happens to match cloaking's cooldown so then cloak again. That gets the Vulcan to full chain before the enemy shoots at all.
But it still takes the Vulcan a while to actually drill through the shields. With any amount of enemy evasion, it barely keeps up with shield regeneration. It mostly doesn't break through for damage by itself, just keeps the shields down. It needs other weapons or drones for the actual damage. And a Defense Drone II versus a Vulcan is a hilariously spectacular fireworks show -- but effective on the part of the drone.
It's not the best weapon in the game. I'd rather have a Glaive Beam. Same deal of 4 power and a long charge and relying on other weapons for support, but deals its damage more immediately and effectively across multiple system targets. I'll see how the Vulcan does on the flagship, but I think I'd rather have a Glaive there too to whack both the missile weapon and shields together.
The Vulcan feels like overkill win-more. If you can turtle long enough to spin up the Vulcan, you can turtle long enough to win in any number of other ways, including beam weapons which do the same job faster and more reliably. It's still very good if you don't come across beams or enough shield-stripping for them, though. It's one of many solutions.