And this is where I get really confused. Does this mean that a computer won't natively understand / recognise the USB device? I'm looking at the cheaper ones on ebay which use the CH340G which need drivers.
Are these additional drivers only for communication when programming, or would any computer that the keyboard is to be used on need those drivers too?
The FTDI chips and the CH340G are both USB VCP to serial bridges. They allow the microcontroller to use it's serial UART to talk to the PC via a Virtual COM Port (VCP). Driver software must be installed in order for the OS to communicate properly with the bridge chip and create the virtual COM port. The drivers are specific the the bridge chip used. The arduino requires these a driver as well, but is usually installed as part of the Arduino tools installation.
A USB VCP to serial bridge chip does not support the USB HID protocol used USB keyboards. In other words, you could not use the ATMega328P and CH340G bridge chip to create a plug and play USB keyboard.
Note: Most of the Arduino's have used a USB VCP to Serial bridge chip for programming and communications purposes. The morerecent UNO replaced the dedicated bridge chip with an ATMega8U2 with custom firmware that functions as a bridge. The 8U2 could be reprogrammed to act as a USB HID to serial bridge allowing the Arduino to act as an HID keyboard. The Arduino Micro has an ATMega32U4 and can also be programmed to act as an HID keyboard.