If anything my seagate goes into sleep when connected to the PC but never when connected to the wii. Infact the only 'glitches' I get are on some 2 player games eg NFS nitro with both players playing.
Couple of ideas
1. Unless you made the entire drive WBFS, there is no reason why you cannot connect it to your PC to make changes. (hope I didnt misunderstand your question there)
2. Are you sure you made the WBFS partition primary and active during setup?
I set my seagate up using favs' guide here: favs hdd guide