TL/DR version: yes, spore burst can, but not as well.
Long version: The AVs in the LRSF have, like the vast majority of AVs, just the basic boss sleep protection. Neither spore burst or mass hypnosis will sleep them with one shot, but both will do so under domination. Thus, it is certainly possible to sleep the AVs with it.
However, it won't do as good of a job. In many ways, spore burst is the second best control set sleep, after mass hypnosis. It has a better duration than salt crystals and is ranged, and it doesn't have the annoying tiny tick of damage that lets the enemy shoot at you before the sleep is applied like flash freeze. It also has half the recharge of those two powers - in fact, the same recharge and duration as mass hypnosis. However, what it doesn't have is mass hypnosis' lack of aggro (it also has slightly shorter range). This will make using it to perma sleep the phalanx considerably more dangerous to the dom. As well, plant control lacks the backup tool of mesmerize - this power allows a mind dom to spot sleep (in a single shot, even outside of domination!) any AVs that the AoE sleep misses. Without that tool, again it becomes a more dangerous task.
So, yes, my guess is that under domination you probably could keep the phalanx slept with spore burst (ain't tried it myself of course). I'm guessing it would be considerably more difficult and dangerous, however.
@MuonNeutrino
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I was looking at this too the other day for the same reason. As far as I can tell, it has the same stats (recharge/mag/duration) as mass hypnosis, but like muon said, the set lacks the backup of mesmerize. I forget where, but somewhere else I believe that the activation time is not as good as Mass hypnosis which was supposedly a problem (doesn't make it impossible, just harder). I've never done it before, but I thought AV's had more protection than mag from domination. I was under the impression that it took more than 1 application of the mez.
In any case, when I get my dom up to those levels, I'm very interested in trying this out. Let us know how it works out for you. When I do run it, I plan to bring another dom to help, so it may not be an issue, but I'd still like to know.
Spore Burst works fine. Sometimes you do get unlucky and miss the same Hero twice, but it's not like you don't have 7 other villains backing you up? Communication is key.
Does anyone know if spore burst sleep the FP AVs at the end of the LRSF? Or just Mass Hypnosis?
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@Virlou