No it will not work there is no active device. The reason the neon works is because as soon as the capacitor charges up to the neon's conduction voltage it will dump all the caps energy flashing once and then staying off till it's charged up to it's conduction voltage again, the neon tube is acting like an arc timer with the R/C values, no such effect can occur with an LED.
The simplest solution would be to actually buy blinking LED's, they have the blink circuitry built right into them.
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20 bucks for 100 of them.. These will not work on 1.5 volts though you're going to have to use at least two cells.