I foresee some problems. You *can* install WUBI to an external drive, but it
is going to present you with a couple because usb drives are removable and
because the file system in WUBI is inside a large file.

If you have more than one USB device attached WUBI may not work. The
bootloader will be on your C: drive on the MBR. It will point to WUBI
thinking that it is fixed in that location. However, if more than one device
is attached the bootloader may point to the other device. The bootloader is
set to a fixed location, but usb devices can be removed and that could be a
problem in some circumstances.

Secondly you will not be able to access the file system on the usb device
other than through WUBI because WUBI is just a large image file, like an
ISO. Externally you won't see your home folder just the image file. You can
add to the device from Windows but they would not appear in Ubuntu as they
would be outside the image file. You can add to the device from Ubuntu and
they would not be available in Windows because Windows cannot access inside
the image file. Copying your /home folder to Ubuntu while your in it is not
going to work very well either because some files will be in use. It is a
Catch-22.

A better solution would be to go for a full Ubuntu installation on the
external drive. If you have a boot manager, ie. can press a key on boot up
to choose which drive to boot, then write grub to the external drive and not
the MBR of the C: drive. This way, you can control things better. You can
copy the home folder without difficulty using the Live CD which won't work
for WUBI because the file system is hidden to you. If you don't have a key
to press to get a boot manager then you can write to the C: drive MBR, just
knowing that it may give you problems if more than one device is attached.

WUBI is not meant to be a substitute for a full installation. It is meant as
a way of testing Ubuntu that gives more of a full experience than the Live
CD which cannot be written to. You can use it in the way that you want, but
it is awkward to say the least and in the long run it will limit you more
than you realise.