Will the gaussian kernels in this fragment shader be computed for every fragment?
It depends. On a desktop, if the Gaussian function is always called with the same arguments, the shader compiler will probably optimize it so it's evaluated only once. On a mobile platform though, the compiler has less time to do optimizations and might miss it. Either way, you can confirm by looking at the generated assembly.

Note that Aras Pranckevičius of Unity wrote a GLSL optimizer to address the problem of sub-optimal compilers on mobile: https://github.com/aras-p/glsl-optimizer

That being said, regarding your sample code, I would definitely at least expose (1.0 / sqrt(2.0 * 3.141592 * deviation)) as a uniform.