Can you play Shadows Call with no unit?

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

According to the official RiftJudge FAQ #9478:

Q: Can you use Shadows Call to draw without any friendly units? A: No, you cannot use Shadow's Call if you have no friendly units.

According to Rule 355.10, a game object mentioned in the text of a spell is a target unless it falls under specific exceptions. Shadow's Call instructs you to "Choose a friendly unit." Because this choice is not part of a cost, a trigger condition, or a replacement effect, and it is not programmatically selected, the friendly unit is a target of the spell.

Since the spell requires you to choose a target to play it, you must have at least one legal target (a friendly unit without [Temporary]) available on the board to play Shadow's Call.