Ehh no. In school in Argentina you are taught that the whole continent is called America, then you have subcontinents in it (North/central/south), and I would guess other south american countries are the same. If you want to say citizen of the USA in Argentina you would call them yankees.
I can't think of the last time I needed to describe myself as being from the continent, but if you really want to call yourselves Americans, I say go for it. People can call themselves whatever they like.
Still, I can't help but notice Argentinean newspapers using americano to refer to refer to things from the US.
In general, we use north american when referring to the USA. America is used to note the continent, like the south american soccer teams cup, "Copa Libertadores de America" (liberators of America cup).
La Nacion uses americano, but has to specify "continente americano" as if simply saying "americano" wouldn't be clear to readers. They otherwise also use estadounidense and norteamericano.
Neither appears to ever use "americano" by itself to refer to people from the continent, but if you're telling me that if you walked up to someone on the street and said you were an American and they would interpret that as you from the continente americano, then I believe you.
I'm still going to use the demonym American for myself (as everyone gets to pick their own demonym in their own language) and use it to refer to people from the US, but if you to call you an American, who am I to say no? You can call yourself an American, I can call myself an American and everyone is happy.