Assuming low angle of attack & anhedral wing configuration. (and as a consequence of natural left yawing moment)
Simple answer: no, it wouldn't, otherwise it wouldn't be certified if it behaved like that :)
The real answer is the same as to why nearly all high-wing aircraft have anhedral. Yes, anhedral angle creates the 'adverse' roll effect, but it is made to counteract the excessive positive effect from all other factors, namely the wing sweep and the high-wing configuration itself. (The latter effect is more complicated than the usually assumed 'pendulum' effect: it has more to do with the added drag and cross-flow effects of the sideslipping fuselage (see, for example, here)).
As always, too much of a good effect is not good at all: excessive static stability causes oscillations, in this yaw/roll case known as Dutch roll, so anhedral is used to reduce the overall effect to a reasonable but still positive level.
Dihedral of an aircraft's wing will only make it more stable (dynamically and statically) about its longitudinal axis. As aircraft starts to bank, the lift vector over the down going wing will be more vertical that the lift vector over up going wing, meaning that greater force to lift the dropping wing will be produced than the other which will create opposing moment and tends to stabilize the aircraft.
Now, as right engine fails, the aircraft will yaw to the right (nose right, tail left), depending upon the magnitude of the power setting of the remaining engine. This induced slip will as a result have three consequences:
1) Left wing (outer wing) will have a greater velocity than the right one (inner wing) and it will cause a lift imbalance to be generated by the wings. This effect will make the aircraft bank to the right.
2) Since An-72 is a swept wing aicraft this effect will also play a role: the outer wing (left wing) will be more perpendicular to the oncoming airflow causing a greater lift to be produced. The right wing will be less perpendicular to the oncoming airflow meaning less lift will be produced. This is because the velocity written in lift equation should be perpendicular to the airflow, if it is not -> less lift will be generated.
3) Probably not applicable for An-72, but some aircraft will cause an aerodynamic shadow to occur and even greater lift to be lost over the inner wing.
Since none of all these 3 effects are dependant upon dihedral, the aircraft will surely banked to the right in the stated situation.
Due to the dihedral design of the wing the opposing moment while banking to the right will not occur, which means that harder recovery to straight and level flight will take place.