Yes, they can. Grape skins—white and red—contain tannin compounds, so a white wine that has been left on its skins for an extended period (often to amplify its aromas) will pick up tannin, too. Oak wood also contains tannin compounds, so wines aged in oak barrels (especially if the staves have not been aged for a long time) can sometimes taste tannic. Excessive tannin in white wine can make that wine feel coarse, raspy, and rugged, and is very undesirable.

—Karen