You connect it when you want, really.
But there are things to know:


1. If you have a Non-WiiU formated drive connected while you are in WiiU menu, it will ask you to format it. Just select Cancel.
2. You can bypass the WiiU menu to boot directly to vWii by holding B on the WiiU gamepad until you select the Mii profile. it will tell you "Wii mode will be launched". No Format HDD warning will be displayed.
3. You can "hide" the Non-WiiU drive by corrupting the partition table signature. it's called "UStealth" drive. The USBLoaders are compatible with stealth'd drives so you don't need to worry about it anymore. No More format warning message, and it works on vWii. But the drive will not work with all homebrew (no EmuNAND, no emulators, no Computer access !!! the drive is hidden to your computer too). There's a homebrew on vWii to switch stealth state of the drive.
4. USBLoaderGX has a known issue with some recent HDD. it will freeze at initializing the drive. a workaround is to plug the drive when you see the 20sec countdown instead of plugging it before booting the console.


So, it's up to you to decice what you think is best.
if USBGX is compatible with your drive:
- do nothing, select Cancel to format message
- use UStealth

if USBGX has init issue with your drive:
- connect it when launching the loader
- it doesn't prevent you from using ustealth at the same time to prevent the warning on WiiU menu


UStealth drives are compatible with:
Nintendont
USBLoaders
some Emulators
UStealth switcher

 

it wants to format it to WFS (not a format that can be read/accessed by anything else than a Wii)
There's no table partition, the ENTIRE drive is a single block of encrypted data. there's no partition at all.



ALL consoles (Wii, PS3, PS2, Xbox, etc.) expects HDD to be FAT32.
FAT32 is used universally across palteforms and consoles.
just use FAT32 for Wii too.

WBFS is old, deprecated and corruptible.

FAT32 is not only compatible with emuNAND, it is also with ALL homebrew : The Homebrew channel, emulators, gamecube backup launchers, media players, computers, games, etc.
you want to store a 9GB video bluray dump? buy a dedicated HDD for your consoles, and one for your computer. don't mix them. 99% problem solved.
Users are making things overcomplicated.