Trying to flash ATTiny85 bootloader using FT232R in the Arduino IDE
A bootloader is a program that gets loaded into the bare microcontroller to handle a number of low level tasks. One of those tasks is the ability to load a program over UART (serial).

As such, the bootloader can be loaded into the microcontroller using a AVR programmer. Once this has occurred, you can then easily load in programs with the FT232R.

It is possible to use the bitbang mode on the FT232R to load the bootloader into an Arduino board, hence replacing the AVR programmer. So, it can work but it isn't easy.

As suggested by per1234, there is some instructions on how to do this to an Arduino Diecimila on the Adafruit website: Programming the Arduino Bootloader
In general the full page has a lot of useful information: Full page