Did Canada's role in the crisis help their identity/autonomy that they were striving for?
For the purposes of this question I'm going to split the identity from the autonomy.
It is important to note that at this point in history, Canada was fully autonomous. Canada and the other dominions (Australia, New Zealand, etc.) had been granted independence in foreign affairs by the Statute of Westminster in 1931. That being said, Canada had yet to assert their autonomy in a meaningful way by 1956. Though much is made of the fact that Canada declared war on Germany independently of Britain in 1939, our somewhat delayed declaration was really a foregone conclusion. If Britain went to war, we would go to war to defend our closest ally.
Thus, the Suez Crisis constituted a genuine shift in Canadian foreign policy. For the first time, Canada made it explicitly clear that they would not be backing Britain in their latest adventure. The days of "Ready, aye, ready" were long gone. Israel had already invaded Egypt in October 1956, and in November Britain and France landed troops along the Suez Canal. However, when the Soviet Union threatened the the UK and France with nuclear war if they intervened, it was clear that something had to be done. Before the fighting got out of hand, Canadian External Affairs Minister Lester B. Pearson suggested that a United Nations force be sent to the region to separate the two sides and implement a cease fire. The creation of the United Nations Emergency Force (UNEF) was unique at the time, and Pearson was awarded the Nobel Peace Prize in 1957.
The Suez Crisis was an important demonstration of Canadian autonomy, and could be regarded as a maturation of Canada's role as a middle power in international diplomacy.
Canadians have been known to regularly cite peacekeeping as one of our enduring contributions to the international stage. It is a point of pride for many Canadians that Canada is known around the world as the founders of peacekeeping, as well as one of the greatest contributors to peacekeeping missions over the years. The idea of Canada as a nation of peacekeepers, an "honest broker", a middle power, etc. has become so ingrained in the national consciousness that some historians are now challenging what they call the "peacekeeping myth". Eric Wagner breaks down how Canadian peacekeeping missions were based on strategic rather than moral foundations in the "The Peaceable Kingdom?". The argument is that missions such as Cyprus were more about defending the interests of NATO - in that particular case preventing a conflict between two NATO countries, Turkey and Greece - than they were about moral indignation.
It is worth noting that, like almost all expressions of Canadian nationalism, the emphasis on peacekeeping is as much about differentiating Canada from the United States as it is about taking pride in Canadian contributions.
TL;DR: Yes, it was an important step for Canadian autonomy. And yes, Canadians consider the Suez Crisis/peacekeeping in general to be part of who we are, even if that's less than accurate.