No.
Firmata does communications between PC "applications" and hardware connected to the Arduino, more-or-less making the arduino "invisible". The Arduino CAN communicate with the PC using formats/protocols OTHER than firmata. For example, the "Serial Monitor" capability of the IDE does PC/Arduino communications in a very "Raw" form. It does not use Firmata. The IDE also communicates with the Arduino for purposes of uploading sketches, and that doesn't use firmata, either.
You can do exciting and useful things on an Arduino for YEARS without ever using Firmata.
WRT Firmata, the IDE is the tool that is used to load the Firmata protocol onto the Arduino. The IDE also does many things that have nothing to do with Firmata.