Yes the number of Qubits used to represent the problem scales polynomially with the bit-length of the input integers.

However, annealing here is used as an approximation of a brute-force search. If you demand a sufficiently exact (i.e. non-approximate) result, run-time is still going to grow exponentially with problem-size, thus for 2048-bit numbers the D-Wave machine will maybe not finish by the time the universe ends :)