A splitter will only work in conjunction with other aerodynamic devices. A splitter is intended to be part of an aerodynamic system that induces downforce via ground effect. The idea is that the splitter prevents air from diverting from the front of the car and going underneath the car and instead diverts most of that air around the side of the car. The idea of ground effect is to starve air from underneath the car to create an area of lower pressure under the car therefore sucking it to the ground. I don't think the underbelly pans under the 944 are there for ground effect as they have holes in them. Also the area behind the belly pans are not covered so would destroy any effect a splitter and the belly pans might have. True ground effect cars have perfectly smooth undersides with no holes or vents underneath.
Maybe the factory cup cars did have extra belly pans attached to the underside of the car which didn't appear on production cars in order to create ground effect, but in terms of splitters, I'd be very surprised if they have any effect whatsoever. I've read that some people say they notice more front end stability once they've fitted one, but I think that is just in the mind after they've installed one - like you manage to convince yourself your car runs better after a service or you can feel a power increase once you install a K&N filter. Your seat of the pants is not a very accurate gauge of minor improvements in anything.
Splitters look cool but I wouldn't expect a sudden improvement in handling after fitting it - unless of course you make a completely flat underpan along the entire length of your car.