Yes it does and Meredith's Red Lyrium was just like any other.
"The soldiers looked like normal men and women, but they rained down blows so hard it numbed my arm through my shield. It took me three minutes to kill just one, and he only stopped when I cut off his head!"
http://dragonage.wik...ar_Foot_Soldier
"The templar bastard cut him down without a word! A dozen of us against three of them, and we never got a strike past their shields. They're stronger than any man I've known. The templars swung full tower shields of metal like they weighed nothing."
http://dragonage.wik...mplar_Guardsman
And those are only the most normal looking Red Templars. I shouldn't have to explain why a Behemoth is superhuman.
The simple fact that Grey Wardens can sense and be sense by Darkspawn is already evidence of how the Joining alters their bodies.
Then there is Avernus' potion which was created after extensive experimentation on Grey Wardens and whose purpose is to tap into the potential inherent in Tainted Blood and give the Warden who drinks special abilities.
This, added with Morrigan's comment of how Grey Wardens have increased stamina is sufficient evidence to believe that the Joining turns Wardens into quasi-superhumans.
On the first part i'm skeptical,i don't know how much credit i can give to codex of inexpert people about red Lyrium especially when in game red templars are nothing special but i'm willing to dismiss it as a form of segregation gameplay/lore.
The fact is that red lyrium is not the basic taint and it make people insane so any magical improvement they gain is overshadowed by the cost they have to pay for it.
Meredith had powers that were unique and the idol was channeling red lyrium, it was an elaborate artifact to with whom she had the possibility to fly and use several others magical properties never used by regular red templars.
On the second part i disagree since those are not evidences that demonstrate any physical improvement the GW gains from the taint or any super human power, it merely show that the taint has magical powers.
As far as i'm concerned the dark passage is the only ability of the power of blood which improve the warden skills permanently and without costs,all the others are just magical non permanent powers that require a cost.
Morrigan sarcastic comments aren't an evidence thus i don't see why you view GW as superhumans?
When they can just sense darkspawns at the cost of being sense in return....