No, Squiggy, that replaces the unit with a fresh unit and would break the triggers that were doing stuff to the old unit. The "Unit Takes Damage" event he mentioned above does not work for generic units or even variables (at least in the GUI), it has to be a specific unit placed in the World editor.
I thought that since a unit's corpse is still technically the unit, you could just set the unit's life to 100%, but that just created a corpse with 100% of the unit's life.
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revive priestess
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Events
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Unit - Sorceress 0003 <gen> Dies
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Conditions
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Actions
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Unit - Set life of Sorceress 0003 <gen> to 100.00%
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Unit - Move Sorceress 0003 <gen> instantly to (Player 1 (Red) start location)
LOL, to make sure that whatever unit showed up was still the same sorceress, I had a trigger that would make the unit do some animation (Spell Attack), out of curiosity I set it off and the corpse model was replaced by the sorceress model, but it was unselectable, just like a corpse usually is. A ghoul could even use cannibalize on it.
So it looks like you are going to have to replace the unit, but before that, like at map initialization, set a unit variable to that unit (Set foo[3]=unit 0021 <gen>). You will have to change that trigger event "Unit Takes Damage" to something more generic like "unit is attacked" followed by the conditional "Triggering unit is foo[3]". You will also have to use that conditional in every other trigger that acts on that unit specifically. I am sure "unit is attacked doesn't take care of all instances of "Unit Takes Damage" (does AoE and stuff like standing too close to a unit with lightning shield count as attacks? Not all attacks cause damage either) so you will have to get creative with the events, conditionals and actions. Maybe using Hero Units would be easier if you have a lot of these sort of triggers. Anyways...
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Untitled Trigger 001
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Events
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Conditions
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(Triggering unit) Equal to foo[3]
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Actions
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Unit - Replace (Triggering unit) with a (Unit-type of (Triggering unit)) using The new unit's default life and mana
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Set foo[3] = (Last created unit)
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Unit - Move foo[3] instantly to (Player 1 (Red) start location)