Replacing several FP operations with a single integer OP can only improve performance.
It depends on the context. In the case of a GPU, floating point resources are great and integer operations are limited, your statement is false.
Depends on the GPU, too. Some of the more popular mobile GPUs don't even have integer ALUs anymore.
Some GPUs need to emulate integers with floating point operations, so you basically end up with the same shader bytecode like before (or even worse) when using integers.
At least we can all rest easy that GPU manufacturers will provide drivers which, if they claim to support integer math, will emulate it with uncompromising accuracy at the highest performance possible.
Your statement is only true for CPU operations. Modern GPUs have their hardware and drivers optimized for floating point operations.