Do I get to draw a card if I'm out of runes?

No, you do not draw a card if you are unable to channel runes.

According to RiftJudge FAQ #5452: "No, you do not draw a card if you cannot channel. You simply do not channel at all."

If your rune deck is empty and you are instructed to channel, you simply do not channel any runes, and the game continues without penalty or additional card draws.