Air conditioning and electricity are suplied by the APU, not only by the ground units. For engine start up you must use the air presure(the startup motor is pneumatic not electric), that's why you don't have air conditioning till the engines are running, but you can have it till the moment that you begin pushing back. Also low cost companies try to save every cent so they don't use the APU till they have to start the engines. This can be pretty unconfortable when you have more than 28C inside, but they don't care too much.

Edit: redaction.