It's possible, but there is no direct evidence.
As a Maia, Sauron was certainly capable of using ósanwe. As the former lieutenant of Morgoth, he would have known that forcing secrets directly from an unwilling mind was impossible.
In like manner, extortion of the secrets of a mind may seem to come from reading it by force in despite of its unwill, for the knowledge gained may at times appear to be as complete as any that could be obtained. Nonetheless it does not come from penetration of the barrier of unwill.
There is indeed no axan [rule or law] that the barrier should not be forced, for it is únat, a thing impossible to be or to be done, and the greater the force exerted, the greater the resistance of the unwill. But it is an axan universal that none shall directly by force or indirectly by fraud take from another what he has a right to hold and keep as his own.
He would also, however, have been aware of Morgoth's attempts to dominate lesser minds, as detailed in "Ósanwe-kenta".
He found that the open approach of a sáma of power and great force of will was felt by a lesser sáma as an immense pressure, accompanied by fear. To dominate by weight of power and fear was his delight; but in this case he found them unavailing: fear closed the door faster.
Therefore he tried deceit and stealth. . . . For he would come by stealth to a mind open and unwary, hoping to learn some part of its thought before it closed, and still more to implant in it his own thought, to deceive it and win it to his friendship.
. . . In this way he won entry into many minds, removing their unwill, and unlocking the door by the only key, though his key was counterfeit.
The main evidence that I have found of Sauron using ósanwe with regard to prisoners comes from the Witch-King's threat to Éowyn at the Pelennor Fields.
"Come not between the Nazgul and his prey! Or he will not slay thee in they turn. He will bear thee away to the houses of lamentation, beyond all darkness, where thy flesh shall be devoured, and thy shrivelled mind be lift naked to the Lidless Eye."
There are two main problems with this. Firstly, it is a threat. The Witch-King, by virtue of his high position and because of being a Ringwraith, would have known something of Sauron's ability to carry out such a thing. However, this quote may not be strictly literal for the purpose of intimidation. Secondly, he may have been speaking about turning Éowyn into a wraith, as was attempted with Frodo. She would then have been under the direct dominion of Sauron, as Gandalf describes to Frodo in Rivendell. In such a case, the victim would keep the universal ability to close her mind to ósanwe, but would appear to be more vulnerable to Sauron's direct control.
In the case of Gollum, we have very little direct evidence. Gandalf implied to Frodo that he was physically tortured at some point, presumably in Mordor.
"He only wept and called us cruel . . . he whined and cringed, and rubbed his long hands, licking his fingers as if they pained him, as if he remembered some old torture."
In the same conversation, Gandalf states that "the Dark Power was bending all its will" to bring evil creatures to Mordor and that the Ring would leave Gollum "open to the summons" of Sauron. As a Maia and Ringbearer, Gandalf should be able to estimate Gollum's condition fairly well. So at some point, Gollum was receptive to Sauron's ósanwe; this, however, could change at any time by Gollum's refusal.
Their [Incarnates'] bodies being of Eä are subject to force; and their spirits, being united to their bodies in love and solicitude, are subject to fear on their behalf. . . . Upon the body and upon the indweller, therefore, such pressure and such fear may be exerted that the incarnate person may be forced to speak.
Sauron may have sought to accomplish this with Gollum through pain and fear.
Ultimately, while we know that Gollum was questioned in Barad-Dur, possibly by Sauron himself, the exact methods are unclear, save that they were unpleasant.