Only one model of Rolex watch, the Oysterquartz, has ever had a battery. This watch was produced in limited quantities from 1970 to 2001 and was removed entirely from Rolex's catalog in 2003.
Rolex made a name for itself producing fully automatic timepieces that did not require an external power source. It had been doing research on electro-mechanical watches since 1952 and filing patents since 1960. The OysterQuartz was the only commercial result of this research, however.
The presence of a battery in a Rolex model that is not an OysterQuartz is a telltale sign that the watch is a fake.