Can Emitter Follower BJTs work with large signal?
The emitter follower, because of the negative feedback is pretty linear amplifier and is used for large signals all the time. Of course, if you want it to be even more linear, some special schematics have to be used but it actually depends on the application.

Also, the emitter follower has voltage gain less than 1 but the current gain is pretty high and as a result it is amplifier.

In your question you didn't specify what exactly the signal and load is, but on 10Vp-p and 50ohms of load, you probably will need some push-pull emitter follower as a power stage.