I've never had any issues with damaging ROM chips when I removed them. I just wet the contacts with flux, blow the hot air over it, and gently lift the ROM with tweezers. I also don't clamp the PCB down, so if any pins are still attached it'll just lift the board rather than rip the pin off.
But, I have ruined a few rather expensive PCB's from tweaking other components near the ROM. Especially these new WD 2060-800022 boards where the ROM is right next to the main IC. So reading in place would be great in my opinion.
I've got a similar looking setup to what /u/pc3000 posted a picture of, but I've never found it very effective at reading the chips in place.