Nay, nay. The car uses the charger to run the CC and the EVSE doesn't know the difference between that, and charging the car. To the EVSE, the car's charging when climate control is running from it. So telling the EVSE to "stop" will probably make the car now think it's unplugged. Not 100% on that (I've never used the buttons on an EVSE with them - just use the upgraded EVSE "brick" at home), but it's probably better to just turn CC on and the car will override the charge if it's set to do so (I think remote climate control always does).
Only weirdness with being plugged in is that *only* air-conditioning will run from the charger while the car's charging when you're inside the car - but NOT heating. If you turn the car on while it's plugged in, and try to use the heater, you'll just get cold air! Maybe a 2011 thing fixed for 2012 or a firmware update I don't have, but kinda frustrating. I've got far too much experience sitting in the LEAF for 4-6 hours at charging stations waiting for a charge while on a weekend road-trip to/from San Jose...