Can I play Shadows Call without having a unit on the board and still draw 2 or must I have a unit on the board?

No, you cannot play Shadow's Call if you have no friendly units on the board.

The card instructs you to "Choose a friendly unit without [Temporary]." That choice is a target (Rule 355.10), and you must have at least one legal target to put the spell on the Chain. The draw-2 only happens as part of the spell's effect — you can't bypass the targeting requirement just to get the cards.