No, I looked.
I wondered if you had.
From the very informative page to which you linked:
Item:
As of August 3, 2005, the Netherlands had 13 military personnel for the NATO Training Mission Iraq (NTM-I) and 4 troops in the Irak region for SFIR.
Item:
As of mid-July 2005, Norway still had approximately 10 staff officers deployed to Iraq. These Norwegian personnel form part of the British and Polish divisional headquarters staff.
Item:
As of July 9, 2005, the Estonian unit deployed to Iraq was the 34-strong light infantry platoon ESTPLA-11; operational control of which rested with US CENTCOM. In addition, at least one Estonian Officer was known to be serving with the coalition forces' information department.
Item:
As of early July 2005, Latvia had 136 troops in Iraq.
Apart from the UK, the largest number of non-American troops are from non-NATO nations. But yes, technically, there are 14 member nations represented.
It's kind of like saying that the French were part of the coalition fighting Great Britain in the early days of the American War of Independence because Lafayette and 12 of his friends came over to join Washington's forces.