So I am upgrading my father in law's machine from an Old P4 to a newer AMD 5000.
If I just pull the disk out of the old box and into the new one, is Ubuntu (Feisty) still going to boot/work, or am I better off reinstalling everything from scratch ?

It will still work, but if there are other differences (for example, new machine has ATI GPU while old one had Nvidia) then an updating of the drivers will usually be in order, but the machine will certainly be bootable and you will be able to make any necessary changes without too much trouble.

Good news, will save me quite a bit of work.
The video card will go from the old box into the new one, so I am safe from that standpoint.

There might be slight differences in geometry calculations from one computer and to the next computer. Manufactures recommend to format on the new system and I also suggest the same thing. It is best to buy a new hard drive and format it on the new setup. Then copy the files over. It will be more work, but it will minimize any problems in the future such as boot problems. It will also provide a backup if anything goes wrong during the transition.

The video driver for X11 can be changed to vesa, but some people have problems with this. Include modelines for the monitor to make vesa work reliable at any resolution. The gtf utility can help you make modelines for your monitor.