Can sperm live for two weeks?

Unlikely: Very unlikely that sperm would live more than 3-4 days.

Possibly, unlikely: When sperm are deposited into the vagina they quickly move into the cervical mucus to avoid the acid ph of the vagina. Once in the cervical mucus the sperm swim through to the uterus and up to the egg over the next few days. Good cervical mucus is usually only present for 1-3 days before ovulation. It would be rare that the mucus would be good for 2 weeks and the sperm survive - not impossible.