If the split vent is open, there is flow out the split vent. And it soundls like your injection technique runs the pressure up in the inlet - which will result in an electonic flow controller cutting back on gas coming into the inlet - so the only thing that can go out the split vent if no carrier as is being introduced is sample. You do not have a splitless injection. Can you have a splitless headspace injection? Depends on what you are doing. If you are doing a syringe injection of a small enough voume that you can deliver the sample over a short period of time then yes, you can. If you are using an automated headspace sampler, you may not be able to do this.
Tell what kind of equipment and the technique you are using. The devil is always in the details.