If the first proposition (2+2=4) is apriori analytic, then so is the second (2+2=5); the first happens to be true, and the latter false.
This suggests that you're simply asking whether apriori analytic propositions can be false, given that most examples show only true ones. They can be, a proposition has to be judged to be true or false; so there are true propositions, as well as false propositions; a proposition is not one that is neccessarily true, but a question that is proposed, so the first proposition properly posed is:
Is 2 added to 2 equal to four?
to which, the answer is true; and
Is 2 added to 2 equal to five?
to which, the answer is false.