Aha! Good question! In this case the answer is usually yes. Since the forces at work here are shear < perpendicular to the shaft of the screw> rather than longitudinal. You could almost think of the screws as pins going into the bottom of the platform. the wieght of the platform itself is going to keep the caster from just falling off, the screws simple keep it from sliding away from where you want it placed. Now, if you were using particularly large diameter casters, so that the torque of rotational force incurred when running into an object, say a screw left on the deck or something like that, was enough that it might over come the down force of the mass of the platform, and transfer into longitudinal pull on the screw, it could become sufficient to overcome the "grip" of the screw making it necessary to use bolt through the top of the platform.
It's much easier to draw a picture of this than to explain it.
I hope I didn't confuse with that little diatribe.
Short Anwer- Yes screws are fine in most instances, unless you are planning on running the platfrom over rough surfaces really fast.