part of the gown, the gloves, and the instruments are the only things that are considered "sterile." Scrubs, caps, loupes, etc are in this kinda weird middle ground. if a doctor inadvertently touches his cap after gowning he has to re-scrub or change gloves. The point of a cap, which is not sterile, is simply to keep hair and dead skin from falling into the field. You won't often see a surgeon head butting a surgical field, unless s@#t has really hit the fan. Scrubs are also not sterile, which is why they are kept completely under the gown.
At the same time, most institutions have rules about where scrubs can be worn, many prohibit wearing scrubs and caps outside of patient care areas, and want them all to come from inside the hospital (no taking scrubs/ caps home). Most places dont care if doctors wear their scrubs or caps as long as they remain inside "patient care areas" (the hospital)....I can't really comment further on scrub policy, which is the realm of infection risk control doctors and administrators.
Many surgeons have snazzy cloth caps. As a matter of practical importance, I would advise you not to ask about the sterility of their caps, or point out the losing record of their favorite college football team.
Enjoy your stay in the OR. If you get sprayed with blood, try not to pass out or cheer like the front row at a Gallagher concert.