You're supposed to do (a+b) to demonstrate the effect, because floating point subtraction that results in a number near zero is sensitive to rounding (worst case, a non-zero number gets you a zero number), which can introduce a huge error when a and b are very similar numbers.
IEEE 754 doesn't (usually) distinguish between different NaN encodings for the purposes of semantics--if the result is a NaN, it doesn't specify which NaN the result is. Most hardware vendors implement a form of NaN propagation: when both inputs are NaN, one of the operands is returned, for example, always the left NaN is returned if both are NaN.
As a side note: all compilers I'm aware of make almost no guarantees on preserving the value of NaN payloads, hence they consider floating-point operations to be fully commutative, and there's no general way to guarantee that they evaluate in exactly the order you specified.
IEEE 754 operations are nonassociative, but they are commutative (at least if you ignore the effect of NaN payloads).