Applying drugs to brain via scalp (transdermal)
The short answer is no, it will take forever for a drug to pass through skull bones.

The usual reason to apply drugs on skin is if you want them to act right there, on the skin. Acne creams fit here. You need less drugs, you get where it is needed sooner, and you have fewer off-target effects, when compared to taking them by mouth. The brain is not "right there", so this scenario does not apply.

The second reason is convenience. Some drugs cannot by taken by mouth, because they would be degraded by the stomach or guts. In most cases, the drug has to be given through painful, expensive injections. But if such a drug does pass through skin (usually when it is a fat-loving small molecule), you may get away with applying it on skin. Testosterone is one such drug. However, it usually doesn't matter whether the skin you are applying on is close of far from the target organ. The drug will be taken from the skin by blood, get to the heart through veins, and then spread to the whole body, eventually reaching the target. There is no reason to shave your head, since it will go through the same detour before reaching the desired destination.