For the sake of the question the plane is fully capable of inverted flight, no problems with engines etc.
Background of the question is the observation that the airflow around the wing must also invert the direction. If I look from the end of the right wing in direction of the fuselage, I see the air moving around the wing counterclockwise, while inverted it must spin clockwise. So at one point the relative air flow must cease completely on average, there is no difference anymore between top and bottom of the wing.
While the airflow is not turbulent, this should feel for the pilot like stalling because there is no lift, also the wingtip vortices should stop. The "no lift" position should be somewhere near the point when the plane has its wings vertical.
So once a pilot brings a plane into a roll, what exactly happens? Is it a smooth transition from full lift to no lift to full lift back or is there a sudden loss of lift which must be overcome by spin inertia? I have also the suspicion that trying a roll with a too high angle of attack risks a real stall because the restart of the circulation around the wing is hampered.