We're talking about the same molecule that serves as an excitatory neurotransmitter in your brain. It turns out that if you eat a lot of it, it's possible to get a headache (other people claim other ailments). Not much is known about the specifics of the mechanism, but it's not that implausible.
The blood-brain barrier makes this completely implausible.
Does it? The blood-brain barrier lets lots of stuff pass, primarily restricting large molecules and hydrophilic molecules. Some, like glucose for instance, are specifically pulled through. I would expect amino-acid monomers would go right through. Prions, misfolded proteins consisting of many monomers, certainly manage to pass through, or no one would ever get the associated diseases.
The blood-brain barrier makes this completely implausible.