Does pre-ejaculatory fluid (pre-cum) contain sperm even if one has not ejaculated in months?

Absolutely: What you call precome, can definitely contain sperm, even though in lower numbers than an ejaculate. Good luck from nyc.

Yes - it may: 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/