No, Schism doesn't allow you to manifest powers while unconscious
Though the split minds created via Schism act independently of each other, the "second mind" should still be affected by conditions that apply to the character (with the explicit exception of haste effects). Nothing in the wording implies that one mind could be unconscious and the other not; if the character is unconscious, both minds are. If the character naturally falls asleep, both minds should be sleeping.
If affected by the Sleep spell, the schism would end; that's a compulsion effect, and if you fail a save against a compulsion effect, Schism will end automatically one way or another, so you can't use Sleep to induce a sleeping state and keep Schism's benefits.
So how can you manifest powers while unconscious?
The only means of manifesting while unconscious I was able to find in the Psionics Unleashed or Psionics Expanded: Advanced Psionic Guide handbooks is the Lucid Dreaming trait, which allows access to your powers while dreaming:
... you are aware of when you are dreaming and have access to your power point pool and powers known while in the dream.
Though the downside is that points spent while dreaming aren't recovered when you wake normally, so that somewhat offsets one of Guarded Sleep's benefits.
Casting the net a little wider (Dreamscarred produced a lot of psionics-based splatbooks), Psionics Augmented: Feats and Powers adds the feat Unconscious Unconditionally, providing the benefit that:
The first round after you become unconscious, you can use the Unconditional Power feat to manifest a power as if you were stunned.
Which I would rule as allowing a character to use the feat to manifest a power just after falling asleep. You'd need to be at least a 13th-level manifester to do it, though, since using Unconditional Power increases the power cost by 8, so the total cost of manifesting Guarded Sleep this way would be 13 points, and it does require investing two feats in it.