With full speed brake, the roll rate will also be higher, it is not limited to the partial speed brake condition.
In the partial case, the opposite wing spoiler drop couples with the roll side spoiler rise, giving an increased rate, as well as the increased loading of the outer wing for a given condition, which increases the roll response of the ailerons alone. Yes, the AoA is generally higher with the speed brake up, and that acts to mitigate the aileron effectiveness to a point, but mainly at the very high AoA case approaching stall, not at the normal AoA's in operation.
With full speedbrake, the aileron effectiveness alone increases roll rate, if the AoA of the outer section is below stall AoA.
The above is not necessarily true for the B777, 787 or the Airbus, where the controls may change the scheduling of the spoilers and the aileron deflection for a given operating condition. Having said that, the B777 roll rate is increased with spoilers up... On the A320, recall that the roll scheduling was done by the position of the flap handle, and if the TE flaps were stuck at full flap, then repositioning the flap handle would lead to divergence with or without the autopilot engaged.... due to the excessive roll sensitivity from the spoiler deflection with a full flap position. (HDA323 - OEB117)