Can Severe Insomnia Lead to Blackouts?

It could happen -- but dissociation happens a lot because of a trauma -- and that can be something that has happened long ago in the past. A person can have DID and it can just start up one day without anything specific triggering it -- but they mostly have some history of abuse or other traumatic stuff.

Speaking from experience - an angrier, more anxiety-ridden, ultra-paranoid, bordering-on-violent version of myself appears when I'm not getting enough sleep, so it seems perfectly logical to me.

Maybe the tendency for dissociative identity disorder is already there (ie, the trauma of an abusive childhood), and the insomnia is the tipping point?

In m family we deal with a bipolar disorder that exhibits as schizophrenia, down to hallucinations. Sleepless nights are a trigger. Once the balance is restored the memories are either gone or seem like a dream--s6

Hi there

Some narrative research material I suggest you look into is the Nightmare on Elm Street, particularly it's (rather shitty) remake.

Why do recommend a bad movie, you ask?

Because it (briefly) touches upon the adverse effects of voluntary sleep deprivation (in their case, to avoid a sleep demon, in yours, the occupational hazards of being a lab rat [oh, dear, this isn't a story about me is it ]). One of the things they mention is something known as microsleep, where your body just checks out briefly in a sad attempt to get some Zs.

Also, they did some pretty interesting studies on putting rats in no-sleep environment (like a bowl of shallow water or a rocker).

http://en.wikipedia.org/wiki/Microsleep
http://en.wikipedia.org/wiki/Sleep_deprivation#Other_effects

Long story short, sleep is like oxygen, food, and water--organisms don't do well about it for very long. There are correlations between psychosis and sleep deprivation, and microsleep is evidence that your body knows how to turn itself off when it's too tired. I wouldn't be surprised if a blackout could happen. Perhaps throw in some stimulants to assist the character reach that blackout point, since the body has a few counter mechanisms of its own.

Good luck, I think you have a cook, Jekyll and Hydeian premise going on here.

Happy writing.

EDIT:
One more thing, take note that this alter ego uses the same, sleep deprived body. I'd have a hard time suspending disbelief if "Mr. Hyde" fan function just fine in a ragged body and mind, while "Dr. Jekyll" is limited to the biological crutch of sleep. Unless he gets his sleep after Mr. Hyde is done with his shenanigans? IDK, we'd probably have to read the story to get a taste for the dynamics.

Speaking from personal experience here.

I had a medical condition that, for about 4 days, made it impossible to sleep more than 10 minutes at a time. By the end of this, I became emotionally unstable (burst into tears a professional setting because I was having a hard time finding a book in the office library). So, while I don't know about blackouts, I would believe a significant shift in mental functioning, and loss of basic emotional control. Something a bit longer would probably push someone over the edge.