Sure. Molecules effuse quicker at higher temps because they have an increased KE, meaning they move quicker and thus collide with the pore more often resulting in quicker effusion. If pressure increased, the molecules would collide with the walls of the container more often and thus the pores more often.
As for a pressure differential, the tendency is to move from high pressure to low pressure. Kind of like how a roof is blown off a house when wind blows over the top of it, reducing the pressure above. So I would assume that an increased pressure differential would increase the drive to move to low pressure.
