So long as the item you select can be turned after installing, and can't move about, it might work fine. Keep in mind that the reason for turning the center in place is so it will be dead concentric with the spindle. .
While Jim's point about concentricity and roundness are correct, working between centers that do NOT run properly is not a good idea. Often the reason for installing centers is for second operations. Centers are typically used for grinding, for example. If the centers are not concentric with the part (such as when the one in the headstock runs out), when the part is placed in either dead centers, such as are normally found in grinder headstocks, or in centers that run properly, the amount of error is now present. Assuming one has left .010" for grinding, and the headstock center was not concentric by a like amount, there would be no material for cleanup.
Harold