I don't think so, unless you'll allow one of them to be a negative mixed number.
A mixed number is the sum of a whole number and a fraction.
(Whole number-A + Fraction-A) + (Whole number-B + Fraction-B) =
(Whole number-A + Whole number-B) = (Fraction-A + Fraction-B)
Right away you see that this can't be equal to 2, because we have the sum of
two whole numbers ... which must be at least 2 ... and then some more.
But if you'll accept one negative mixed number then it's easy:
( 6 1/2 ) + ( - 4 1/2 ) = 2