only if it is fully equipped - with all control and navigation means and armaments,"
"armaments" is probaly a smoke screen. The Mistral has a pretty basic self-defence suite - couple of Simbad SAM and a couple of 30mm Breda-Bofors. The Russkis could do way better than that with their Kashtan
What they may want is the Thales MMR-3D NG multi-role radar.
That was certainly important to the ADF as a whole, but I honestly think the Navy just wants a chance to have a carrier again :)