A couple points:
Any spell that targets your mount and NOT you would seem to be game over. IHS won't work then. So... um, yah. (just from spells listed on the last page or two, a quickened TK trip on the mount will bring you down)
Get an intelligent mount with IHS? Remember, I did leave space for Leadership in there. Your mount can be any appropriate mount for an effective level 17. You're good to go here. If you want, swap Leadership for the Dragon Cohort feat and get a Wyvernn (Advanced 4 HD to be big enough) Warblade 2/Unarmed Swordsage 2 as your mount or something. Slap some grafts on him while you're at it. Go nuts.
Second, while I'm in awe of you guys' knowledge and ingenuity, hasn't the topic changed a bit?
The title refers to "viable, magic-less character"s... not "viable if that character brings 17 different flavors of cheese, and no one else does". If all the other characters bring that level... the GM will have to tune the encounters appropriately...
Except while he's using cheese, he's handicapping himself by choosing not to use magic. Using magic would be far more optimization here, and thus not equivalent.
So the ultimate answer is "Yes, it's viable, as long as everyone else holds back."?
Sorry if I missed something... not much sleep.
He's holding himself back by choosing to ignore magic items... so yeah, others would need to hold back equivalently.