Will a virtualised copy of Mountain Lion on recent hardware run the Adobe CS5 Suite with comparable performance to an Early 2009 iMac?

This is difficult, at best, to tell without the specs on the current Mac and what Mac you are planning on getting. Even then determining how well the Adobe apps in question will run is entirely subjective. How "well" something will run depends on how the person using the virtualized macOS perceives it to run.

That said, you should likely not purchase an entry level model of Mac (EG cheapest, iMac, cheapest MacBook, cheapest Mac mini, etc) with base level storage and RAM.

That said Parallels (and for that matter VMware Fusion) will both allow you to virtualize macOS on macOS and provide the ability to run those Adobe Apps that your father uses.

Note that transplanting an image of the old Mac's drive to use in the virtualization software might be more problematic than just installing a fresh copy of Mountain Lion in your virtualization environment, updating it and then using Migration Assistant to copy over his settings and apps. However other people may have better advice on that front.