The broad answer is "probably yes" but it depends on how you define the question.

1. Is the EU a unification project? I think it is - and it's quite clear from the text of the Maastricht Treaty and the statements of politicians at the time of its signing - but it's definitely a disputed point (hard to cover the dispute in any detail without breaking the rule against present-day events though). It also depends on what you define as unification - whether that would a single federation, or if the existing situation of a common market and currency already qualifies.

2. How far are you willing to stretch "peacefully?" The other examples of continent unification I can think of are the colonisation of Australia and the Spanish control of South America (which, if we include the personal union with Portugal, covered the whole continent). The former did see many conflicts with Aboriginal tribes, but these were mostly local in nature and involving settlers rather than the British army or police forces, and so you could perhaps call it "peaceful" at a stretch. The latter of course involved many bloody wars against the South American kingdoms and is not at all peaceful.

3. The EU does not technically span the whole continent. Aside from those which the EU wants to join at some point but have so far refused (i.e. Switzerland and Norway), those which are leaving (current events alert) and those, like Serbia, which are not yet members but would like to be at some point, there is an elephant in the room: Russia. The European part of Russia comprises about four-tenths of Europe's total land area, yet Russian membership of the EU has rarely even been contemplated. This is chiefly a legacy of the Cold War and the EU's roots as a Western European political project - and therefore Russia is conceived of as a distant rival rather than another European country.

My personal view is that for the purpose of historical comparisons, the EU is best considered as a large, loosely organised empire, in some ways comparable to the Holy Roman Empire or perhaps Austria-Hungary. But really, these comparisons are fairly useless as the EU is historically unique - such a large union of so many different countries has never been attempted before.

I'd like to suggest Kwame Nkrumah's attempts to unify African states, in 1958 and formally in 1963, with a pan-African movement as being the first attempt to unify a whole continent peacefully. With the speech "Africa Must Unite", Nkrumah fought to bring newly independent nations together through the aims of "one man one vote", which would bring all African nations to share and debate how best to progress their shared resources and interests, newly free from colonial rule.

In 1958, Nkrumah, the newly elected Ghanain leader, hosted the leaders of Egypt, Ethiopia, Liberia, Libya, Morocco, Sudan and Tunisia to discuss how best to achieve progression for the rest of the continent and fight the exploitation of their peoples by colonial rulers. The result of which was the leaders signing the Charter for the Union of African States whose stated aims were to:

• create better lines of communication and co-ordination between leaders, reducing incidents
• defend the sovereignty and independence of all states
• eradicate all forms of colonialism
• ensure the provision of Human Rights for all citizens
• raise living standards for all people

with provision for potential new members.

As new members joined, two blocs formed with competing ideologies of how best to progress their shared aims. The mainly sub-Saharan bloc who believed in a mainly economic linked continent, not unlike the recently ratified Treaty of Rome which created the European Economic Community. While the mainly North African states believed a federation of states would be better equipped to ensure progression.

In spite of the cold war, foreign interference, assassinations and reliance on colonial institutions, the Organisation of African Unity were able to cement independence for all of its member states to varying degrees, the end of apartheid, the development of the African Development Bank and finding a voice within the UN. However, due to the previously mentioned interference, the organisation was not without its criticisms; mainly due to the lack of a standing army and impotence when confronting civil wars, dictators and human rights abuses from leaders.

In 2002, the Organisation of African Unity was disbanded and reformed as the African Union to better streamline the OAU and African Economic Communities treaties into a single organisation.

Kwame Nkrumah - Africa Must Unite http://feintandmargin.com/wp-content/uploads/2015/04/Africa-Must-Unite.pdf