You can, but why would you want to? It will have no useful or practical effect, except perhaps to provide you some satisfaction that you are doing something claimed to be helpful by some anonymous voice on the internet. Its also a (minor) disease vector - but so are the other things you are doing so I assume that's an acceptable risk (and really, its a pretty minor one).
Quality Feed. Fresh clean water. Frequent water changes. Practical shelter with good ventilation. That is all.
I see, daily, people repeating things on Youtube, Facebook, etc said to be natural remedies based on some poorly understood science. The dosage is the poison. Underdose for an extended period of time, you do nothing but create resistant varieties of whatever. Overdose, and there are real potential health consequences. But just because garlic or red pepper flake, or oregano, or cinnamon or whatever have some antibacterial or antifungal compounds in some trace quantity does not mean that adding some tiny amount to your bird's food or water will somehow be a miracle cure all (or even an effect preventative). Were it otherwise, you could walk by a pharmacy counter and be suddenly cured of every malady, just by the trace parts of purified compounds floating in the air at parts per trillion concentration. That's not at all how nature has been shown to work, since time immemorial.
