Use RS232 - RS422 Converter with Encoder
Is it possible to read the encoder output from the PC with this converter?

No.

An RS232 to RS485 converter is just a level shifter - it has no impact on the data protocol being used.  PCs have no built in way to read quadrature encoder signals, so no level shifter will ever get the encoder to work with a PC - not on USB, VGA, RJ45, DB9, or any other connector.

Will it burn the encoder?

Probably not.  If you keep the converter set to the correct direction, it won't break the encoder (if you flip it to the wrong direction, it'll output negative voltages which might break the encoder)

Is there another way to read the output?

What you need is:

1) A way to convert the quadrature encoder signals into a serial protocol that a PC understands.

2) A connection to the PC that uses the appropriate logic levels.  USB is probably the favorite here. 

There are a couple of solutions, depending on your skills, budget, and project.

1) Use a direct encoder to USB converter, such as RB-Phi-94

2) Use an absolute encoder with an SPI output (e.g. AMT20).  Hook it up to a USB-SPI adaptor (E.G. MCP2210).

3) Get a microcontroller board such as an Arduino and build your own quadrature to serial converter.  There are some helpful directions to get you started, but this is still a significant undertaking.  I won't go into detailed instruction on this here because you'll probably need to do a lot of research to make this happen.