Yes. That is the purpose. It will except on most divisions, but not all. As of additions and multiplications, hard to say. I would say it depends on application. I.e. 2*3, or 0.5+1 will not except, but when adding vastly different values in magnitude, or ones that have a lot of nonzero in significant digits, it will except.
It is a useful tool in some applications. I never used it personally tho, even in implementation of interval arithmetic.