No. The coil is a mile of copper wire wrapped by a huge magnet. When you send a deliberate signal to the coil, it moves in response to the magnetic field produced. Without a signal, the coil doesn't move as there's no frequency to make it move.
If the speaker is emitting cracks/pops without a signal from the deck, then there's something else interfering and creating a signal. Usual suspect is a bad ground on the amplifier creating backfeed, abraided/ungrounded/unshielded signal wires allowing certain frequencies to enter etc.
Usually it is a burned voice coil, but only usually. Sometimes it is something else. Check all wiring, move any signal/speaker wires away from power cords etc. If it's a household powered sub, check the outlet it's plugged into, the plug should be tight, not loose to plug in. Check the deck power outlet too.