Yes, it will work fine, technically. But your Windows install won't work.
You will have to format and reinstall windows.
You can't just move a drive with an OS installed from 1 pc to another.
Well, you can, but it is a royal pain, and it will be buggy. Best just to format and start over.
If you just want to install it as a second drive for storage, no problem.
Does this mean that I could hook up my old IDE hard drive (with XP on it) and DVD Burner with the IDE cable without incident?
You should have no problem connecting your drive and DVD burner as long as you have the Master/Slave or Cable Select settings configured correctly on the devices. You will be able to see and use the IDE HDD as a storage device just fine. If you intend to dual boot there will be issues with drivers installed in the old XP installation that will make if difficult to do without reinstalling XP.
You could connect the IDE drive as the master and the ATA DVD burner as slave in the new computer. If the chipset on the motherboard is from the same maker (ie via , nvidia) there is a good chance you XP will boot. If not then you will have to run a repair on the OS.
Best of luck