Can candidiasis occur around the mouth, not in it?

Yes : A condition known as angular cheilitis or perleche is a condition where deep cracks or splits occur in the corners of the mouth. Perleche (or angular cheilitis) is caused by the infection of the mouth corners ( labial commissures) by the fungus Candida Albicans or by a bacteria.

Probably not..: Candidiasis is in most people's mouths but is kept in check by bacteria and saliva. I have heard of patients having a red crease from the yeast, but no signs of candida in the mouth. When a culture is taken it is positive for candida in the mouth.