Can a blown head gasket make engine oil leak out?

No, head gasket work with the cooling, however it has been known to mix with the oil and make it milky, i guesss if to much mixed in the oil section then yes cause oil seal, valve cover gasket, all could fail at that point and leak but the oil you see should be white'sh brown. here are the signs of a blown head gasket back up of cooling in overflow, milky oil on dip stick, and the number one pick of signs is wet spot on block right around the head.