HTTP header: These are small and so it's unlikely you'd overcome the overhead of sending it to the gpu. I could be wrong in some cases though, like servers which have to parse hundreds of HTTP headers at once (I imagine this kind of thing must happen somewhere...)

JSON: Seems unlikely. Nested structure like that often has bad perf on the GPU. You might be able to organize it to parse a lot of the same kinds of JSON files though.

A decent way to think about the GPU is that it's a couple thousand (for good GPUs) processors of power equivalent to a 1st gen pentium (there are many quirks, like they hate branching, but this is an ok way of thinking about the compute power).

Unless you can actually leverage that parallelism -- and there's a lot there -- it's not going to be a net win. It's also fairly expensive to send data to the GPU, nothing that bad, but enough that for anything fairly small you're way better of staying on the CPU