If on birth control can you get pregnant from precum?

Unlikely. Fluid prior to ejaculation comes from a gland in the urethra so it rarely contains sperm but can especially if the man recently ejaculated. Also, some men can't tell pre-ejaculate from rapid ejaculation and that's why withdraw method is unreliable birth control.
Low possibility. Birth control when taken as prescribed with perfect compliance (ie- not missing any days) have 0.3% failure rate whereas in an general population there is a 9% failure rate (most likely due to non-compliance, missing pills etc). Pre-ejaculatory fluid can contain sperm and it may lead to pregnancy. However, if you are taking your pills as prescribed, you have a low risk of getting pregnant.