Yes, the backup utility under system settings will backup everything but trophies.
To backup your trophies, go to trophy collection, press Triangle, and choose sync with server.
Make sure you also have a device (downgrade dongle) to enter Factory/Service mode also. That does not come with the e3 flasher limited. That is the step that will format your HDD. A FSM firmware install will format the drive.
It also does not come with a micro sd card and a usb flash drive.
You can check this list
for devices to use as a downgrade dongle.
Or if you have a phat PSP 1000 model, you can use PS3Jig.