The normal gap permitted is 10mm - which is to allow for floor coverings - leaving a true gap of approximately 3mm.
The limitation being required as the door will normally drop into the gap under test so transferring the gap to the head which is the most onerous location.
The issue of smoke control is a hazy one - the method of testing smoke control does not require the bottom edge to have a tested seal, it in fact requires that the bottom edge is taped over. This assumes that cold (more correctly termed ambient) smoke will stratify and that air will be drawn toward the fire from underneath the door - negative pressure hence the smoke will be kept away from the bottom edge.
Hadn't thought about testing an architects head for a smoke seal - always had it in mind that one would be more use for hard body impact testing!