Could a woman be pregnant if she had unprotected sex during the 2nd day of her period?

Possible: Its possible but not probable. If you do not want to get pregnant, protect yourself.

Yes: Pregnancy from exposure on any day of a woman's cycle, including during menses, has been documented. However, those with irregular intervals/cycles would be the ones most at risk. Those with predictable patterns are less so. Pregnancy requires a fertile egg become available to a fertile sperm.