Was Canada in the coalition of the willing?

A CBC report based on U.S. diplomatic cables obtained by WikiLeaks suggests that Canada played a greater role in the 2003 invasion of Iraq than the public statements of its leaders previously suggested: 

On March 17, 2003, two days before U.S. warplanes launched their attack on Baghdad, prime minister Jean Chrétien told the House of Commons that Canadian forces would not be joining what the administration of then U.S. president George W. Bush dubbed the "coalition of the willing."
Chrétien's apparent refusal to back the Bush administration's invasion, purportedly launched to seize weapons of mass destruction possessed by Iraqi ruler Saddam Hussein (which were never found), was hugely popular in Canada, widely hailed as nothing less than a defining moment of national sovereignty.
But even as Chrétien told the Commons that Canada wouldn't participate in Operation Iraqi Freedom, Canadian diplomats were secretly telling their U.S. counterparts something entirely different.
The classified U.S. document obtained from WikiLeaks shows senior Canadian officials met that same day with high-ranking American and British diplomats at Foreign Affairs headquarters in Ottawa. The confidential note, written by a U.S. diplomat at the gathering, states that Foreign Affairs official James Wright waited until after the official meeting to impart the most important news of all.
According to the U.S. account, Wright "emphasized" that contrary to public statements by the prime minister, Canadian naval and air forces could be "discreetly" put to use during the pending U.S.-led assault on Iraq and its aftermath. At that time, Canada had warships, aircraft and over 1,200 naval personnel already in the Strait of Hormuz at the mouth of the Persian Gulf, intercepting potential militant vessels and providing safe escort to other ships as part of Operation Enduring Freedom, the post-Sept. 11, 2001, multinational war on terrorism.
The U.S. briefing note states: "Following the meeting, political director Jim Wright emphasized that, despite public statements that the Canadian assets in the Straits of Hormuz will remain in the region exclusively to support Enduring Freedom, they will also be available to provide escort services in the Straits and will otherwise be discreetly useful to the military effort.

It's not really clear whether the Canadian ships and surveillance aircrat conducting counterterrorism activities in the Straits of Hormuz at the time did, in fact, carry out any activities that contributed to the effort in Iraq. As one high-ranking former defence ministry official quoted by the CBC puts in, "[W]ho knows whether in fact we were doing things indirectly for Iraqi Freedom? It is quite possible."
It's certainly not unreasonable to suspect that Canada may in fact have played a larger military role in Iraq than a number of declared members of the Coalition of the Willing.
The other interesting aspect of the story is that U.S. officials were apparently fairly indifferent to Canadian military support, hoping instead for political cover: 

A former senior Canadian bureaucrat said: "The Americans knew we were stretched to the limit on the military side, and they really just wanted a political endorsement of their plan to go into Iraq."
Former U.S. ambassador Cellucci concurred: "We were looking for moral support. That's all we were looking for.… We were looking for 'we support the Americans.' "

Canada still has several thousand troops in Afghanitan and now Prime Minister Stephen Harper's government was an early and enthusiastic supporter of intervention in Libya, contributing fighter jets to enforce the no-fly zone.