If a person kills themself by shooting themself in their head, they can't come back as a walker, but what about people who died of a brain tumor? Can they come back as walkers or are their brains too damaged?
The Walking Dead franchise is built on the premise that any human that has passed away will be "reborn", until their brains cease to function.
This is very well 'documentated' in Season 1 by
Dr. Jenner (which is also the first time Rick knows that you can 'resurrect' without a bite)
According to the
CDC's reasearch (and Jenner's conclusions)
Any body that has a functional brain is capable of restarting itself, on a basic, very primitive level.
Now, as per the question, you can have a brain tumour in different areas of your brain, therefore as long as it doesn't render it useless it will return. At least, that's what logic tells us.
An example of a brain that wouldn't get rebooted would be a brain of someone who died and suffered an heavy trauma to the head. Have you ever heard of people with memory loss? That loss may be SO severe that one can forget how to use certain muscles, or even become in a vegetative state. On those cases, even if the brain 'reboots', then it's not a threat as there isn't a "communication" between the brain and the body part.