Hi,
Factory Data Reset is nothing but the mobile OS restore point like Desktop OS restore point.
This backup ill be done by the OEM.
Basically in this point, Whatever pre-bundled applications comes with phone remains exist.
Basically you will not be having any user installed apps after the factory data reset.
Again installing an application is user attention process(meaning can be done through Android Applications Manager app, if you customize that, it ill be possible ), cannot be installed silently.