Short answer: no.
An automatic watch doesn't use a battery — it winds itself. As one r/CitizenWatches commenter put it:
"Automatics don't have batteries. They're self-winding — a rotor spins as you move your arm and winds the mainspring." — r/CitizenWatches
That's the whole trick. Inside is a weighted rotor that swings with your wrist and stores energy in a spring. Wear it and it keeps running; set it down for a day or two and it'll stop — just give it a few shakes or a wind and reset the time. There's no cell to replace, ever.
One catch: don't confuse automatic with solar or kinetic. Those are quartz movements that store power in a capacitor or cell — a different animal. A true mechanical automatic has no battery at all.
Want one that runs on movement alone? Our Carnival automatics use a Seiko NH36 — battery-free, just wear it.
Good watches without the bullshit. — One Good Watch