Well, two things have to be mentioned in the answer: First of all, the precedence matters, of course, since if we have a formula like p|q&r, then we first have to decompose the disjunction before the conjunctions. Otherwise, we consider a different formula, and clearly, may get different results.

Your doubt is however less critical. You are essentially wondering how to decompose an equivalence like p<->q which can be replaced either with p&q|!p&!q or (!p|q)&(p|!q), i.e., by a DNF or a CNF. All of these formulas are equivalent to each other, and therefore it does not matter which one you choose for the definition of a "syntactic sugar" operator. Once that is done, however, precedence matters!