The Wall says: Put 1 NW character into play from your hand, knelt as a defender, during any challenge against you. (limit once per challenge) which leads me to believe that it is irrelevant whether or not said NW character has the appropriate icon which is required to defend normally. Is this correct? Will Defenders of the North (STR 8) be able to defend any challenge if I have The Wall, even if I am not running any The North Agendas?

You are correct. This situation (character participating in a challenge without the appropriate icon) is similar to what happens when Walder Frey's passive ability triggers.

And now you know why the Wall can be a big pain in the butt if you are playing against it and don't have non-challenge related location control.....

Definitely a fun and brutal card.