Pichia strains such as SMD1165, SMD1168 can grow in YPD media or even in synthetic complete yeast media that do not contain any biotin. but BMGY specifically include biotin in its composition. I am trying to figure out what advantage does it provide to the media for cell growth. May be I should just go ahead and prepare BMGY with and without biotin and try expressing the clones I have to see if there is any difference.
I think actually there is enough biotin coming from yeast extract and peptone in YEPD to ensure normal Pichia growth. Synthetic complete also contains biotin coming from the YNB. I think the BMGY recipe is directly inspired from the BMG recipe (which contains biotin) only supplemented with yeast extract and peptone. As you said, it might be that biotin is not necessary in BMGY context (just as in YEPD context).