Question about Urgoz

Will giving Urgoz a deep wound be enough damage to then allow Edge of Extinction to trigger?

No.
Edge of Extinction only triggers when things die. It will not trigger for Urgoz until he reaches 0 health, same for all creatures.

EDIT:
If you mean "trigger" as in "will he take damage?" then I would have to say that I do not know. Common sense would tell me that the answer is "No" since deep wound lowers maximum health, not inflict damage. However, I personally have not tested it and nothing indicates that it would trigger it.

Characters who are at full health with a Deep Wound are still considered to be at full health, so skills such as Edge of Extinction will not trigger.

Not to mention it probably wouldn't take him below 90% anyway, what with his HPs...

Deep wound takes 100 health damage away from (max 100 health). So, no.

Deep wound is not damage.