That still wouldn't be valid, since either unsigned integers wrap around on addition (the default behavior of most languages), in which case nonzero values can

That still wouldn't be valid, since either unsigned integers wrap around on addition (the default behavior of most languages), in which case nonzero values can still sum to 0; or unsigned integer overflow raises an error, in which case the transformation is dangerous unless the integers are both strictly bounded in magnitude. Unless the integers were unsigned big-integers, in which case performing the long addition with carries would take Θ(n) time, as opposed to the simple Θ(1) operation of just checking both their bit-lengths.