I am doing kickboxing and am wondering if there's any risk of brain damage even if head hits aren't allowed. Thanks.
Walking on the sidewalk carries a risk of brain damage. Consider that before moving onward.
Any contact sport--and many ostensibly non-contact sports--involves the possibility of an accident involving a clash of heads, a stray limb, or a slip and fall. But I wouldn't classify no-head-contact kickboxing as any more concussion-inducing than flag football, Ultimate frisbee, high school soccer, or roughhousing with your kid cousins. Severe concussions can happen from getting out of bed. The thing to realize about this isn't that all these activities are terrifyingly dangerous but that freak accidents are just that: accidents that are freakish in their improbability, impossible to plan for or protect against. Note that all but one of the low-probability-concussion-inducing-activity examples I've used are from the experience of people I've come into contact with.
The other point to remember is that there's more than one step from sport to brain damage. First you have to get hit in the head. Then the hit in the head has to be bad enough to cause a concussion or split your head open. Then the hit (or multiple hits over some period of time where you don't stop doing the sport) has to be bad enough to cause brain damage. Barring some freak accident, I can't see how such a path seems like a likely scenario. Lots of people kickbox with head contact, for years, without brain damage.
Brain damage can be caused by a lot of things but the main causes are drugs and concussion/compression (usually from boxing or similar sports). If you suffer a compression or concussion, you will have brain damage as a result to some extent. The more times you become concussed and the more serious the hit (to the head), the more serious the brain damage becomes. Sometimes you might not notice it, but the damage is still there and can be detected by psychological tests. Other times it can result in psychosis, depression, loss of fine motor skills or dementia in the long term. The short term effects include short term memory loss and blacking out.
That said, if you are not being hit on the head the chance of concussion/compression is likely to be a lot less. Short of you falling and hitting your head on the ground it is extremely unlikely that you would incur brain damage.
Light contact sparing such as that done by the World Karate Organisation is also unlikely to result in brain damage: anyone who moves the head with a strike gets disqualified on the spot. This type of training (i.e. light contact, not karate) may be a good complement to the no-head strikes sparing, if you are training for self defense.