Can you get pregnant from precum days before your period?

Yes: Anything is possible, but usually less likey right before your period, becuase ovulation occurs about 2 weeks before the period.

Timing is big issue.: Most studies have shown low levels of sperm or no sperm in pre-ejaculate with sperm not being motile (however, don't know how promptly samples were examined). One small study published in 2011 showed that there are some individuals with a high motile sperm count in pre-ejaculate. See: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3564677/