Will a blood pregnancy test show positive 9 days after unprotected sex?

Possible!: Assuming the stars aligned just right and sperm was present in the uterus at the time of your ovulation (even 5 days beforehand!), you could conceive and that would be day 0. Hcg (pregnancy hormone) is sometimes detected at the time of implantation (once reaching a level detectable by your lab ~3miu/ml), which is anywhere between 6-12 days after fertilization. So, yes!

Possibly: If you got pregnant at that time, it might.