24v AC can't be used to drive a single 12v LED for a good reason. The AC voltage is usually measured in RMS (Root Mean Square) and is not the same as peak voltage. With half a wave to light the LED, you would have an "average" voltage of 24v and peak voltage of about 34v and this will fry 12v LED quickly. A 620 ohms resistor above will help but l'd think 1k resistor is safer.
Putting 2 LEDs close together, 1 in reverse from other, will give the illusion they are always lit. If you use only 1 LED, you'll get a noticeable flicker like cheap LED christmas lights.
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What kills LEDs (when charge is flowing through them in the forward
direction) is overheating because of excessive power dissipation,
and as far as heating the LED and the resistor goes, 24VRMS is
exactly the same as 24VDC. Moreover, since each LED is only on 50%
of the time they\'ll each be dissipating 240mW instead of 480.
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