Here in ARN running the APU on the ground except for engine start is not allowed, so we have no problem. If the crew leave the APU running after arriving on the gate they have only themselves to blame.
But, connecting up ground airconditioning and nothing happens. There is an NRV in the ground air connection that stops the ground air entering the aircraft until the packs are off. (the packs produce much more pressure). It is only if this NRV is broken open that there will be a problem, and the ground crew will hear that when they open the panel.
Don't worry about having both connected, it is very hard to damage the aircraft.
But.... do not connect air start air and APU bleed at the same time. This could damage the bleed system, if an NRV was stuck open.