Several Yes's, but with cautionary notes.
First, connection system. I guess your new machine has a SATAII HDD, and it's connected to the SATA0 mobo port. Further, your BIOS Boot Priority probably is set to boot from the CDROM first, then hard drive on the SATA0 port, and no other option. Now, how about your old 80GB drive? IF it also is SATA, you can just plug it into another SATA port. IF your BIOS enables each SATA port independently (not common) you might have to enable that one. It will still boot from the SATA0 port, and your old disk should just show up in My Computer ready for use.
However, if the old one was an IDE drive, obviously you need to connect it there. In that case you will need to pay attention to Master and Slave questions. Any IDE port can handle two devices on the port and cable. If the old drive was the only drive in that system, it probably was set with its jumpers to Master, but check anyway. It should connect to the far end of the 80-conductor ribbon cable. Now check your CDROM drive if it also was on the IDE port. If it was there by itself, it will have been set to Master, and need to be changed to Slave. On the other hand, if you CDROM drive is already on a SATA port, just leave it there and don't worry. Now boot into the BIOS Setup and make sure the IDE port is enabled so it can be used.
Now, IF both the old 80GB drive and the CDROM are on the IDE port, when you boot up Windows probably will re-assign drive letter names. This can cause trouble when your already-installed software goes looking for a CDROM that used to be D: and now has been re-labeled. To check and fix, go into Disk Management. Each drive will show its label. If you RIGHT-click on it one menu option is to change its letter name. The trick here is you can only change it to an unused letter. So if your old drive is now D: and the CDROM is E: and you want to switch that around, you do it in two steps. First you make the old drive into something like J:, then change the CDROM to what it should be (like D
, then change the old drive again to its final name, E:. Reboot to make that final.
As far as booting into your old XP, that can be tricky. As installed on your old machine, it had all the drivers needed for its devices, but will be missing drivers for many devices on your new machine. Sometimes you can fix that by doing what's called a Repair Install from your old XP Install CD. If you are going to try that, I would suggest you disconnect your new drive first, so there is no possibility the Repair Install will do anything to your new drive. After you get XP fixed up and working you can re-connect the new drive. Even to do this you may have to temporarily set in BIOS which drive is being used for booting, etc.
There's another likely problem. The old XP installation, without doubt, will detect that is is now running on a machine with totally new hardware, leading it to believe you have made an illegal second installation of this licensed software. To solve this you would have to phone Microsoft Support and explain what you've done - moved your drive to a new machine, leaving the old machine useless with no OS, and ask them to help you re-authorize XP on the new machine. To avoid confusing them, maybe don't get into the detail that you plan to have two OS's on different drives and plan to use both on different occasions.
So, if you get all this working, one simple way to control the (almost) "dual boot" system you have is to use the BIOS to change which drive you actually boot from. One way to do that, when you want to, is to enter the BIOS Setup screens as you turn the machine on and reset the Boot Priority. Then change it back on a later occasion. But you might get away without that, too. I think there's a simple procedure during the boot sequence where you can push a key to bring up a menu that asks exactly which hard drive to boot from. Look for that in your new system's BIOS manual.