Serrano peppers are a type of chili pepper, and since peppers are a type of fruit, they can absolutely be included as part of a Paleo diet, especially if you relish the spicy stuff.
Aside from being delicious, there is some evidence to suggest that eating hot peppers may confer health benefits that other peppers do not. The capsaicin, which is what gives the pepper its spicy quality, is thought to be anti-inflammatory.
Paleo and Inflammation
One of the major goals to living a Paleo lifestyle is to avoid inflammation. We avoid wheat, sugar, and vegetable oils because those foods are inflammatory, and just about every chronic disease, from diabetes to heart disease to cancer, has been associated with inflammation.
That could have something to do with why eating hot peppers is thought to relieve headaches and arthritis pain and may even be helpful in fighting certain cancers. In areas of South America, where consumption of hot foods is common, rates of intestinal, stomach, and colon cancers are considerably lower than in the United States. Of course, this is nothing more than correlational evidence, and as such, should not be given too much weight, but it is a note-worthy association.
Paleo and an Autoimmune Protocol
Just remember that peppers are nightshades and nightshades don’t agree with everyone. Some people have trouble digesting them, and if you know this to be the case for you, then you should definitely avoid all peppers, including serrano peppers. If you’re unsure about your tolerance for nightshades, the best way to find out is to avoid them for a period of time (usually at least 30 days) and then slowly reintroduce them and take note of how they made you feel.
If you know that you have no problem with nightshades, Mark Sisson has a whole post on reasons why we should include hot peppers in our diets.