Unless if you're on Ozempic until you literally dry out every single fat reserve in your body and your brain has to resort to breaking down the myelin sheaths (something that can happen in ultra long distance running, hence why hallucinations sometimes happen on 100+ mile runes), then the GLP1-RAs wouldn't be able to force the body to break down the fat in the brain.
To the best of my knowledge, GLP-1's have 0 direct impact on brain fat metabolism or myelin sheath breakdown.
Side note, GLP1 based therapies are being investigated for improving brain health and potentially helping prevent the development of neurodegenerative illnesses, potentially because of an anti inflammatory feedback mechanism it activates when its able to reach tissues outside the gut. (natural GLP1 is usually broken down ~5 min in the body after release)
Just to zoom in on this -- the understanding of how GLP1 based therapies work seems to also be evolving to have the benefits primarily be brain-focused. While of course GLP1 interacts in lots of ways with your other organs, but the effects on appetite suppression (and suppression of other urges) seems to be majorly brain based.
Some research into how it might work together:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9455625
In fact I wonder if the negative effects of GLP1 drugs (gastroparesis, GI issues) might be completely gone if we can target the agonists towards the brain only somehow.
I've never heard of this before today, but if it's true then that's terrifying.
When your pancreas releases glucagon, adipose tissue (compromised mostly of adipocytes - "fat cells") respond with lipolysis, converting their stores of triglyceride ("stored fat") into glycerol and free fatty acids, releasing this into the bloodstream. Various tissues use the free fatty acids directly, while others (like the brain) rely on gluconeogenesis to create a source of glucose.
Tissues that store glycogen (muscles and liver primarily) also respond by breaking this down into glucose, but this has quite low energy density of hydrated glycogen compared to fatty tissues, and an adult only stores in the ballpark of half a kilogram. This is sometimes referred to as "water weight".
Another response is proteolysis in the muscles, where muscle proteins are broken down ("muscle wasting") in order to feed energy demands.
Point being, the body does not randomly look for fatty acids in the body to tear down - the process of weight loss is a strictly controlled and centrally coordinated mechanism to maintain a steady energy level in your bloodstream. Your cell membranes are also made of fatty acids so all hell would break lose long before it got to myelin if it just started randomly picking things apart!
When in a high-glucagon and low-insulin state (that is, there is a demand for more fuel in the bloodstream than is present), after the liver has used up its glycogen stores for fast and easy glucose production, liver cells redirect most or all of its oxaloacetate supply to the process of gluconeogenesis to produce more glucose for the bloodstream from free fatty acids and glycerol released from fat tissue, as well as some other non-carbohydrate sources.
In this state, the liver's own cells lack the key incredient to finish metabolism of free fatty acids, where acetyl-CoA is combined with oxaloacetate to form citric acid for the Kreebs/citric acid cycle. Instead, the cells start converting acetyl-CoA into ketone bodies and releasing these into the bloodstream to further increase fuel availability.
Cells with mitochondria can metabolize various things including free fatty acids directly, but free fatty acids cannot pass the blood-brain barrier. Ketone bodies can, and while they have to be converted back into acetyl-CoA to be used, the liver does this to keep the central nervous system alive in a situation where glucose production might not cut it.
You only have high levels of ketone in your body after long periods of fasting/starvation (e.g., 24 hours or more), prolonged exercise or if on a diet that forces the pathway with insufficient carbohydrate.
This is because one of the ketone bodies is acetone, a result of spontaneous breakdown of one of the other ketone bodies. Only the liver can break down the acetone, and as it floats around the blood some of it ends up exhaled.
(At very high levels of ketone bodies you end up in something called ketoacidosis. In this state your blood turns acidic, which can quickly develop into a medical emergency. This mainly happens to those with health issues like type 1 diabetes.)