Having such a tome would spare 18 slots. Scrolls in the inventory are not added automatically to the tome; it must be dragged manually to it in order to add it.
Using up all 20 scrolls will make the tome unusable, but new scrolls can be added to it at any time. Scrolls picked up or bought while the Tome is in the inventory are automatically added to the tome, unless the maximum number has been reached.
The Tome functions the same as the Scroll of Identify; Right-clicking it will cause the cursor to change to "Identify" mode, and clicking on an Identifiable item will cause it to use up one Scroll, and identify the item.
Like individual scrolls, the Tome loses its usefulness if the player rescues Deckard Cain themselves. Since Cain identifies all items for free if the player retrieves him, it is a better use of gold to buy more Town Portal scrolls for a quick trip back to town.