The length of the OEM studs is greater than the thickness of your spacer. Therefore, a portion of the stud will protrude beyond the mounting surface of the spacer. This is a typical 20mm bolt-on spacer. The studs on your car will stick out even further using a 15mm type II (bolt-on) spacer. In addition, some of the spacer mounting nut will also extend beyond the mounting surface.
Wheels have varying amounts of relief machined into the mounting face. Some wheels have no relief at all. This example is a Nismo v2. It has enough relief to accommodate a 20mm type II spacer. Not sure about a 15mm though. You'll have to research further.