Nope. If that's the mission where you assaulted the Psi Disruptor, you had to build Overlords. The SCV with the Psi-Emitter just attracted wild Zerg to your brood.
But hey, I like this idea. It wouldn't work for a bash-em mash-em assault, where you both have bases, they have their hill, and you want that hill because the Psi-Boombox (Radio Not-Free Zerg) is under it. But it would work for crawler missions where neither side has bases and Overlords can only be replenished so fast.
Think along the lines of the first Protoss Mission in Brood War.
Now, killing the Overlords shouldn't bring about docility or cause Zergling squads to rip themselves to pieces.
But say you're trying to cross a couple of blocks in a ruined city with a ragtag band of Marines and Reapers. If you try to cut across the rubble of a football stadium, you will incur the full wrath of a dozen Hydras and more Zerglings, overseen by several Overlords.
However, if you kill one Overlord, nothing happens. Two Overlords, and the Zerglings and Hydras split up into different camps (Maybe the two species don't coexist all that well) All three overlords are killed, and they become more aggressive, BUT LESS COORDINATED. They'll see you and attack from a longer distance, but they won't attack as a group. Three zerglings at a time, or something like that. And they won't pursue.
Boom. You have just turned an ambush that would have slaughtered all of your Marines into something you can walk around with care. Of course, if you take too much time, more Overlords will show up, and maybe some Mutas will drop by to investigate. But a feature like this could add more immersiveness (Just added to Webster's Dictionary) to a level. Combined with having to choose your path through the city, avoiding patrolling Mutalisks, and accessing computer terminals to create distractions or open roadblocks, and this is a level that I'd EASILY play through multiple times.
