Interface a LCD to RS232
If the prolific usb to serial converter outputs "TTL-level" signals (that is Transistor-Transistor Logic) and not rs-232 levels, then yes.

Looking around for the prolific adapter you're referencing (this one?) it appears that it outputs between 1.8V and 3.3V, which should be able to communicate to the LCD backpack you're looking at.  You really want a chip which outputs from 0 to +5V for communicating with that model, but they also sell the 3.3V model. I personally use the FTDI ft232rl as my go-to chip of choice for usb to serial converters.

But I digress, if you're only wondering if the display functions taking input from a computer, then the answer is yes.  I did that to test one of those LCDs years ago when I first got it.

Good luck!  Hope that helps.