Missing photos / Broken graphics card

Hi, I've been using an iMac for a few years and Lightroom 5 has been installed on it for 3 years, using it to edit wedding photos which I take a few times a year.

I normally back everything up in Lightroom every week or so and save it in my external hard drive. I last did a back up after a wedding on 4th August 2017, but my external hard drive is saying that the last backup was done on 3rd July 2017. Lightroom never gave me a message that it was not able to back my photos up. I have well and truly learnt my lesson here: I will be backing up all of my photos to the internet as well as on an external hard drive and maybe even separate memory sticks!!

My iMac presented me with the "grey screen of death" and when we took it in to be "diagnosed", we were told that the hard drive of the computer is fine, but the graphics card needs replacing. My question is this: will I be able to open Lightroom with all my photos once the graphics card has been replaced?