The Old and New Testaments were completed several centuries before Muhammad’s time, so he certainly could have.
There is some evidence that he was influenced by a relative who belonged to a heretical Christian sect, but I do not know for sure if he read the Jewish and Christian Scriptures or just took stories from them.
It’s pretty obvious when you look at it that Islam is a descendant of both Judaism and Christianity – it takes stories about everyone from Abraham to Jesus and adapts them to its particular narrative, then claims the earlier versions were corrupted and its take is the correct one. Someone in the mix (and quite possibly Muhammad himself, if the story of his personally dictating the original Quran is true) clearly had access to at least secondhand accounts of the major Biblical narratives.
Of course, if you accept the idea that the Quran was directly dictated by an angel and therefore is indeed correct in all its particulars, Muhammad wouldn’t necessarily have needed access to the earlier (and, according to him, corrupted) Scriptures in order to record his own – but historically speaking they were definitely available at the time.
Usagi