<<So I am going to download the SP3 to this drive (Drive C), and then install it to Drive F.>>
Hmmm...I don't think that you can do it, if you are referring to installing something on an O/S that you cannot boot into.
SP3 and every other update pertaining to the O/S...needs to install into the O/S booted into.
Ditto for programs...if you are not booted into that O/S, those programs cannot install.
This is because of the dynamic nature of installing files...registry settings and files are modified when installing anything. The only way that a registry from a different system can be modified on another system...involves a process which still would not yield what you desire, since the program files will not install into a non-active O/S.
When you added the drive to another system...it became mothing but a storage container. You can access the files on it, but you cannot install anything or change the registry (with the exception I noted).
Windows must be in an active state...in order to install anything on it. "Active" in this instance means "booted into".
FWIW: I don't know if there is a need to uninstall SP3, unless it reflects some sort of problem. I have reinstalled SP3 several times...on systems reflecting SP3...and never noticed a bubble of any sort. In fact, this is one way to overcome certain problems with XP, IME.
...how do I get the computer to boot the Drive F, to then let it Install the SP3?>>
The only way to get drive F: to boot...on a different system...also involves particular problems. Hard drives cannot just be switched from one system to another...and be expected to boot and perform properly. See Changing a Motherboard or Moving Hard Drive - http://www.michaelstevenstech.com/moving_xp.html
It can be done successfully...on occasion...but it's laborious because of the fact that drivers and settings for a different motherboard/system...are reflected on the hard drive. Bottom line...it's not guaranteed success between two different systems.
I don't know everything and I certainly haven't tried everything with XP...let's wait to see what others think.