The Yeast should win, the cold bacteria prefer warmer temps.
I doubt there will be any issues. I am sure particles in the air drop in the wort while people are brewing without any problems, as well as insects, leaves, etc.
it will grow faster than any other bacteria forcing them out of existence...by this point if the yeast started vigorously your pretty much home free. Now all you need is a brew-cage to keep the daughter out