Does an electric smoke alarm have a battery?

It depends on your city's fire codes, most likely yes. "Wired" alarms could either mean "wired to AC power" or "wired to an alarm panel" or both.

Start by calling your local fire alarm installer or electrician. Assuming that the detectors are wired to a central hub in the house/building (fire alarm control panel), the panel would normally have a battery back-up installed. For individual units wired to AC, having a battery back up would be safer, no matter what the laws. Some units will automatically remind you when the battery is low, even though the unit is on AC power, since the smoke alarm must continue to function if power is off for some reason.