Let's consider unweighted graphs, which is still a hard problem. Say you have an algorithm that solves your problem in time $T(n)$. Then I could solve the MAX CUT problem without such an oracle in time $O(m\cdot T(n))$, where $m$ is the number of edges in the graph.
Run $m+1$ versions of your algorithm in parallel, each of which gets a different value for the MAX CUT from the "oracle". Note that $m$ out of these $m+1$ runs will get an incorrect value from their "oracle", but one of them will get the correct one since the true MAX CUT value must be between $0$ and $m$.
After you performed $T(n)$ steps in each of these runs, the run that found the largest cut will have found the MAX CUT.
So no, in general it does not help significantly to have such an oracle.