What will happen if I drive LEDs in parallel from a TLC5947?

dc42:
If the two LEDs are exactly the same type, then you may find that they share the current quite well. I once took apart a toy light sabre, and it had 16 green LEDs connected in parallel, with no resistors to balance the current. Amazingly, the brightness was fairly uniform across all the LEDs.

They might have been sorted/binned at the factory.

I'm sure I've seen LED datasheets that mention you can order them in matched batches.