Yes, you can actually start the climate control while plugged in. Although its finicky. Simply plug it in, hit charge timer off (if at full charge) and get some blinky blue lights going.
Next, hold the brake, push start, and hit auto. Check energy usage to make sure it went on.
Caution: the harmless, yet startling, to 100% charge time bug causes either the L1 or L2 to increment out of control. Depends on what you are plugged into. Likely due to unplugging the car with it on.
In regards to climate control power consumption, it limits it to your maximum EVSE wattage. Level 1 warms up at around 1KW, level 2 at 3KW. It will never, ever exceed, unless you preheat on battery, which means 6kw is possible!!
Also, with a level 2 preheat, your battery will recharge worse than level 1 until if and when it hits temperature...which is difficult at low temps. I have had a leaf hit good temps at 30F even with level 1, but you need a good half hour!