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

If you are using the TLC5947 to drive a lot of LEDs, then you need to take the power dissipation of the chip into account. For each channel, it is the voltage at the output pin (which is the supply voltage less the LED forward voltage) times the output current. Then multiply by the number of channels you are using.

You may find that you need to reduce the voltage at the output pin to keep the power dissipation within limits. One way of doing this is to use series resistors - which gives you the opportunity to use the same series resistors for balancing the current between the LEDs.