maybe im wrong but i notice when i leave my fat ps2 in a horiziontal position, the video gets somewhat dirty on my tv (lines scroll arcoss my tv screen vertically, but not noticable if u dont pay attention to it), the common problem any fat ps2 has.
but when i leave my ps2 in a vertical position the scrolling lines get less visible.
to answer the question:
i left my fat ps2, hdd included, in the vertical position for awhile, no problem sofar, dont need any support to hold the hdd cuz my network adapter's ****in tough (i had a hard time pulling the hdd out of the adapter one time).
PS2|v7 NTSC|Crystal Chip 2.0 Pro
XBOX|v1.1 NTSC|Xecuter3|200GB Maxtor HDD|XBMC
Gamcube|Not Yet Modded