Is it possible to get pregnant while on your period with pre-cum?

No, not unless...: A woman cannot get pregnant during the first few days of her normal regular periods. However, if she has some spotting and is not on her period, but mistakenly thinks she is on her period, it is possible that she is fertile during the spotting. A urine pregnancy test can be done about 3 weeks after sex, if worried. (Also, it's very unlikely to get pregnant with "pre-cum".)

Highly unlikely: unless the female had an extremely short menstrual cycle. 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/