'Imperialised' is an adjective from empire, sort of. 'Postcoloniality' could be a noun for countries once ruled by the European empires and refers to the period after European dominance.
So, basically, reading between the lines of your convoluticationally anti-simplificated questionation, I think your asking; Is America the ruler of a post-colonial empire?
Yes, but it's changing very fast.
Unlike European empires which physically occupied their colonies, America replaced this with economic occupation. Third world countries' elites were kept Pro-American by ensuring they were personally financially dependant on American deals, finance and support. This was backed up by diplomacy and ultimately with the threat of over-whelmimg military invasion. The American Empire also delivered a little glimmer of hope that, eventually, as long as US needs were met, America would eventually deliver democracy, prosperity and freedom to its colonial subjects. But our dear president George has utterley destroyed this belief in American 'good intentions', right at the moment when America's financial super-dominance was ending. So now the US has nothing unique to offer its colonies except the threat of superior military force, which on its own is not enough to rule an empire.
All empires said they would last 'for a thousand years', but none did. America will be no different. Niether will the fast approaching Chinese Empire.