Nope. Order of evaluation and operator precedence are completely unrelated. They should have been defined to be the same, but instead order of evaluation was left undefined. So if you write ++a + a++, operator precedence means this will be interpreted as (++a) + (a++), not say ++(a + a)++, but it is up to the compiler whether to execute ++a or a++ first, rather than executing them left to right.
Sometimes it helps to test. Which I just did. :-)
Actually the compiler (at least clang) warns about this:
The undefined behaviour stems from the fact that "a" is modified multiple times between the "sequence points" (so it's irrelevant to the actual problem that this happens with ++, --, pre-, or, post-, or in which order) We only can modify the variable safely once on the right side without entering bizarro world.A construct like this certainly can be confusing.