I've been preparing for this question my entire life.
I'm a huge science fiction fan, and I've been known to spend a good amount of time over-analyzing fictional science (e.g. Lucy, G.I. Joe: Retaliation, Inception). So I was super excited to tackle this question.
Miriah, the member of your critique group has a good point. The nervous system runs on electricity; current flow in and out of cells is the primary "language" of the brain. And the amount that neurons are active (how much current flow is present) can have a huge effect on how healthy that individual is. Now, there are several disorders of the brain that involve too much neural activity (which I'll equate, roughly, with too much electricity) in various parts of the brain.
Epilepsy is defined by excessive activity in large areas of the brain: all the neurons firing together. Depending on where this excessive, coherent activity is occurring, patients with epilepsy will have motor seizures, or may freeze in place. Certainly they will lose consciousness. Patients with severe epilepsy may die, due to respiratory distress (choking) or because they enter into status epileptics, which basically is a persistent seizure that doesn't stop without emergency medical intervention. In the case of your alien life form, I'd think the shock of bonding would drive a persistent seizure in your protagonist. Now, if your ship has a medical doctor on board, she'd be able to treat the seizing patient. And if the alien had a dormant state, with reduced electrical activity, I think your protagonist could live for several days. Especially if the alien was able to dampen the normal brain activity of the host body, in order to offset it's presence. The classic example of a decreased brain activity state is during comas, although in some sleep states various parts of the brain seem to have decreased activity (e.g. NREM sleep).
To summarize an answer to your first question: Yes, a person could live and function with extra electricity in their brain. They would likely have some issues, most likely some form of epilepsy (depending on where the extra electricity was localized). The physical symptoms could range from motor seizures (as seen in temporal lobe epilepsy patients), to staring spells, where the patient loses consciousness without realizing (absence epilepsy). One additional note: the heart also uses electricity for communication/function. So your alien life form might want to avoid living outside the nervous system, as disrupting the electrical rhythms of the human heart would have disastrous consequences.
If the alien just wants a body to hang out it, it would be best served by moving into the prefrontal cortex of its host. Living there wouldn't disrupt the hosts bodily functions (i.e. breathing), which are controlled by the brainstem. The alien should avoid the brainstem, unless it wanted to bother with taking over autonomic processes such as breathing, walking, etc... The prefrontal cortex is where what we can refer to as "executive functions" are localized. To give you an intuitive sense for what the prefrontal cortex (PFC) does: its activity is particularly disrupted by alcohol. With that in mind, you won't be surprised to learn that the PFC is involved in things like: impulse control, decision making, personality, social behaviors. Reduced activity in PFC has been associated with certain mental disorders, including sociopathy. So if you'd like your protagonist to start acting in a sinister fashion, disrupting her/his PFC activity would be the way to do it. On the other hand, if you're interested in memory problems, or maybe difficulty with language, disruptions in the temporal lobe might be the way to go.
As you can see by my long response, the idea of an electrical life form taking up residence in the human nervous system isn't a ridiculous idea. The nervous system is built around the concept of electrical connections. I would think it'd be a great home for an electrical organism (after all, aren't we humans electrical animals ourselves?). The one thing to watch out for is the idea of electrical balance. Too little activity: coma. Too much activity: epilepsy or cellular death.
But I'd imagine your alien life form might have (or develop) the ability to regulate the electrical activity in its habitat to reduce the disregulation caused by it's presence...
Okay, so let's say your alien has taken over a portion of your protagonists brain, perhaps by suppressing and replacing normal human electrical activity with alien electricity. Now, without some active prevention mechanisms, the other parts of the humans brain are likely to interpret the alien activity as information (electricity is electricity after all, and the language of the brain). So for example, if the alien is inhabiting the prefrontal cortex, the human might act in a very odd manner, as the rest of the brain tries to interpret the ongoing alien electrical activity (unless the alien suppresses the abilities of cells it's inhabiting to communicate with each other, then see my original comments on decreased activity in the prefrontal cortex). But if you want to have the alien take over the humans body (or part of his/her mind/decision making), one way to make that happen would be if the alien was able to learn and mimic the "normal" human electrical activity in the brain. Perhaps with some learning curve.... Of course, a being made of electricity that could mimic other electrical sources could get into so many things. Brains... computers...