My Sears KS-2 (Ricoh XR 7) can handle non-perforated film, I've used some microfilm in it. The spacing between negatives is not consistent, but the counter and shutter work off the winding mechanism. As AgX said, the sprocket wheel on mine only helps with positioning.
It might be better to buy perforated film if you are unsure of your camera. However, if you must have the non-perforated film, first test your camera. Without film, wind, and fire the shutter a few times (you may want to open the back to watch things move). If it works without film in it, you should be okay.
There may be other issues to consider, however. With no sprocket holes, the film may sit up too high on the sprocket, and if the backing plate does not give enough pressure to keep the film flat in this scenario, you may have negatives that are a bit out of focus.