According to the Catholic encyclopedia --“yes” a body may be possessed; however the soul cannot. This would explain why the girl portrayed in the new exorcism movie–Emily Rose-- could have her body so possessed while at the same time she herself was a very devout Christian. Some feel that she was particularly targeted by the Devil because she prayed so fervently for the youth of her time–late 60’s, early70’s–and lived a very holy life herself despite the degrading morals of her peers. Here’s the Catholic encyclopedia explanation.
Demonical Possession
(See also DEMONOLOGY, DEMONIACS, EXORCISM, EXORCIST.)
Man is in various ways subject to the influence of evil spirits. By original sin he brought himself into “captivity under the power of him who thence [from the time of Adam’s transgression] had the empire of death, that is to say, the Devil” (Council of Trent, Sess. V, de pecc. orig., 1), and was through the fear of death all his lifetime subject to servitude (Heb., ii, 15). Even though redeemed by Christ, he is subject to violent temptation: “for our wrestling is not against flesh and blood; but against principalities and powers, against the rulers of the world of this darkness, against the spirits of wickedness in the high places” (Eph., vi, 12). But the influence of the demon, as we know from Scripture and the history of the Church, goes further still. He may attack man’s body from without (obsession), or assume control of it from within (possession). As we gather from the Fathers and the theologians, the soul itself can never be “possessed” nor deprived of liberty, though its ordinary control over the members of the body may be hindered by the obsessing spirit (cf. St. Aug., “De sp. et an.”, 27; St. Thomas, “In II Sent.”, d. VIII, Q. i; Ribet, “La mystique divine”, Paris, 1883, pp. 190 sqq.).