DIY Electrical Safety
For a safe DIY project, you should keep the monitor and the Raspberry PI separate and in enclosed cases. Each with its own power supply. Ac for the Monitor, Dc for the Raspberry PI.


  would by modifying the standard configuration (how the monitor came)
  make it unable to be PAT tested again?


If you take it apart and modify it then the answer is yes. Or at least unable to pass testing.

You should really stay away from using the 240vAc supply. Are you sure the monitor takes 240v, there isn't an external ac to dc adapter? If there is you may be able to take the dc voltage and drop it to 5v for the Raspberry PI. You will want to keep an eye on the ac to dc converter to make sure you aren't trying to pull too much amperage and it's not overheating. If there is no external or obvious ac to dc adapter, I'm guessing it's a CRT monitor then, and you will need a separate power supply to convert that 240vAc to 5vDc with at least .8amps available, for the Raspberry PI, you have a couple methods of doing this. 


Use an external wall wart and then you will have the 5vDc and 240vAc lines running to your project.
Dismantle a power supply that you use for the Raspberry PI (or build your own) and connect that to the monitors incoming AC, and mount it inside the monitors housing or outside if there is no room. This way you would only have 1 power plug for you project. And if you are able to mount everything inside the monitor, it would look like it is just a monitor. Note that I only recommend mounting stuff inside a monitor as a DIY project. Be Careful!


Another thing you want to be careful of is the electrical noise that the electronics of the monitor may produce. This could cause the Raspberry PI to not work as desired.

Be very careful messing with AC and mains power! And inside the monitor (if you are opening it up) you need to be extremely careful on what you touch. There could be enough power stored in a capacitor to hurt and possibly kill you.