You can install Ubuntu using the Windows Installer (Wubi) on any partition that Windows can see that has an NTFS or FAT32 file system. This includes those on external drives. As long as the computer BIOS can see and boot from the external drive, it will work. Note that external drives that have to be unlocked or simulate a CD will not work.
What happens if you unplug the external drive?
Nothing. You will still be asked whether to boot Windows or Ubuntu. If you boot Windows, no problem. If you try to boot Ubuntu it will complain about not finding
wubildr.mbr (if you have Windows Vista/7/8) or just fail to find the install if you have Windows XP and drop you to a grub prompt. If you made this mistake, you can just reboot.
What does the size of the install matter?
For Wubi, the size you choose is used to create a fixed virtual disk. This is the entire space available to the Ubuntu install. Yes you can access and save data on other mounted partitions, but e.g. if you try to install software or anything on the Ubuntu file system you will soon run out of room with only 5GB. The maximum you can allocate with Wubi is 30GB which is a reasonable amount to try out Ubuntu if you are planning to install a number of applications and store some data.
If you run out of space on the Wubi install, it is possible to resize it with a downloadable script, but it's better to pick a reasonable size upfront.
Why do you need Wubi with an External drive?
You don't need Wubi if you have an external drive. You can just install Ubuntu directly onto the external drive, making sure the Grub bootloader is installed on it (not on your internal drive). Then whenever you want Ubuntu you can plug in and boot from the External. And when it's not plugged in, Windows will boot. This sort of installation is portable to different computers (assuming you don't need custom hardware drivers) and not reliant on Windows in any way.
Note: Make sure you install the Grub bootloader on the external or else you'll have a grub rescue prompt whenever the external is not plugged in.