A potential difference created between the two plates in the photoelectric experiment setup helps to accelerate the photoelectrons, so that all of them reach the collector plate and contribute to the current. In the absence of such an accelerating potential, will there be any photocurrent at all? (Assume the photoelectrons come out perpendicular to the emitter plate.)
Yes, as long as hv > φ
When a photon is absorbed, the electron gains an energy hν, ν being the frequency of the light. If this energy is greater than the work function (hν > ϕ) the electron may get ejected out of the metal surface.
Of course, the electron might lose energy due to collisions and not come out at all, but given that there is a very large number of free electrons available (remember that one molar mass of a metal will contain ~ 1023 electrons), there will definitely be a few electrons which will manage to not lose the gained energy and come out with some kinetic energy.
Assuming the ejected electrons come out perpendicular to the surface (or maybe, as with many experimental setups, the collector plate spherically surrounds the emitter plate), as long as the photoelectrons have some kinetic energy, they will make it to the collector plate in some time due to their speeds, and create a detectable photocurrent.