Yes and No.

Yes in the sense that Liu Bang's parents were commoners. They did not seem to be particularly wealthy, but neither were they very poor. According to Sima Qian's Shiji, it was said that Liu Bang showed no interest in farming and manual labor and was frequently scolded by his father, which would imply that his family probably owned some land.

No in the sense that Liu Bang once worked for the government. Again according to the Shiji, it was said that Liu Bang was very strong so he was recommended to become a clerk and later was appointed sheriff of Sishui (泗水亭長).

It really depends on whether or not you take into account his service to the Qin government. Some scholars don't make this distinction, some do. If you do, then the only real peasant emperor would be Zhu Yuanzhang.