Yes.
The A1311 all use the same power supply.
The A1311 was 2009 - 2011 iMac, 21.5-inch
I recommend that a final check would be to try checking for the troubleshooting LEDs. I think you can see those LEDs, if you remove the RAM access door on the bottom of the display, then plug in the power cord.(No need to try the power button, power should be there when you plug in the power cord!) Get the iMac in an angle, probably laying flat on its back, so you can see inside that RAM area. You SHOULD see the glow of one or more LEDS inside, a bit beyond where the RAM slots are. If you don't see any LEDs inside, then, there's no evidence of "trickle" voltage from the power supply. It needs that to boot up. No LEDS, power supply is dead.