scswift:
Would one LED be dimmer than the other as I suspect, with the other drawing a larger share of the current?
Yes.
scswift:
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?
The voltage drop across both LEDs will be the same, only the amps will be different.