Let's start with what WUBI is. It is a bit of wizardry that creates a large
file in your Windows file system. When you re-boot it offers to load
Ubuntu. But Ubuntu is installed inside the large file and not on a drive or
partition. The boot loader treats it like the file is a drive and mounts it.
Once Ubuntu boots then it appears normal because you are now inside the
large image file. Windows can never see inside the file from the outside. It
can only see the large file. Therefore you can't put anything inside the
file from the outside. That also applies from the Ubuntu Live CD. The only
way that you can add to the large file is from the inside. That presents you
with a problem. You want to copy files to your home folder from an external
source (which is possible), but some of those files won't let you because
they will be in use. You will start getting error messages and will quickly
become frustrated. Data files will not be a problem, but your settings will
be.

If Ubuntu was installed to the external drive not using WUBI everything
would be accessible from the outside because you can see the actual files
and not just a large container file. Then you could copy the home folder
while the files are *not* in use. I would use the Live CD to do that and it
would be easy.

The second problem has to do with the bootloader. A bootloader is a snapshot
in time. It says that this is where Windows can be found and this is where
the usb drive can be found. But let's say that you have a usb key and your
external drive plugged in. Then it may get it right or may not. It does not
guess it just looks where it originally was, but if the usb key is there
then it won't look elsewhere for WUBI. It just gives you an error message.
You would have to unplug the usb key and re-boot.The bootloader is just a
file and it cannot keep track of changes made after the fact.

My advice was to do a regular installation because the file system can be
seen and manipulated from the outside. Whether you write the bootloader to
the default location is up to you. It is just easier to manager if it is
written to the same device as it is installed on from my own experience.

Sorry for making it sound complicated. I hope that by understanding what
WUBI is that you can see how it works. There are additional problems with
WUBI that make it unsuitable. It is a large file that can become corrupted
if the power goes out or you crash. If you are in regular Ubuntu it is not a
large file but a file system made of lots of little files. You may lose
something small, but not everything.