There's no easy answer to this one.

It depends what kind of evidence you want to consider (ie human clinical data vs. animal models) and what you count as neuroinflammation (ie cytokine concentrations, gene expression patterns, peripheral immune cell infiltration).

Human clinical data is sparse, variable and usually reliant on sub-par proxy measures so it's difficult to say. Animal data will tell you they do, but you need to pay careful attention to exactly what each study did, what they measured and whether it's of any relevance to a human disease.

If you want to start reading more about it, review articles can help but they are often specific to a particular pathological setting. To go into the primary literature you really need to pick a specific scenario and read around that.

Sorry I couldn't be any more specific, but there really isn't a short or satisfying answer of any value.