1 + 1 in exponential math can equal three, so this is not actually a good way to phrase the question. Some aspects of our world sum arithmetically, some sum exponentially, some sum logarithmically, some statistically, and some sum in the frequency domain. I think we all get the point, which is to ask about logical impossibilities, but the answer when one just considers the math actually suggests an answer.
We humans tend to think that what we experience on a daily basis is a logical necessity. In math terms, this was exemplified by the belief that Euclidean Geometry couldn't NOT be true -- everywhere and for everything. This was actually the example Kant used. Of course, less than a half century later, non-Euclidean geometries were developed that were self-consistent, demonstrating Kant was entirely wrong about the "logical necessity" of any form of math. And then our universe ended up following non-euclidean geometry, just rubbing the noses of necessitarians in their error. (Note that in a space of varying non-euclidean curvature, angles do not sum arithmetically either, for yet another example from our world.)
MATH, it turns out, can be done in all sorts of exotic and unique ways. Which of them are instantiated in the world -- is CONTINGENT, not necessary. And yes, a world could exist where exponential summing was common rather than an unusual exotica, and 1+1 = 3 on a pretty regular basis.
Your bigger question has to do with logic, and whether logic is necessary, even if math is not. And if logic IS necessary, would it then precede and constrain a creator deity? Alternatively, of a deity created everything, a PantoKrator, why would that everything not include logic?
Well -- it took a century and a half after showing that math is purely discretionary, but logicians are now pretty much agreed that LOGIC is also discretionary: https://math.vanderbilt.edu/schectex/logics/ If logic is contingent, then a creator, a PantoKrator, can in principle specify the logic that a world follows. And also could have different parts of a world follow different logics. Which we pretty much knew, given how quantum mechanics follows different logic than macro scale matter.