Would one LED be dimmer than the other as I suspect, with the other drawing a larger share of the current?
And come to think of it... If I were to try to measure the voltage drop across the LEDs, what would I read, with the anodes and cathodes connected like that? Would it be the average of the two voltage drops? Or the smaller of the two?
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.