No, New Coke had a "lite" feel to it which classic, even with HFCS, does not have. New was rather like Pepsi (deliberately so).
I believe what Coca-Cola did was gradually change the formulation in Classic Coke to the point where what we have now is essentially what used to be New Coke.
The ingredients in Classic Coke changed from: Carbonated water, sucrose, caramel…to Carbonated water, sucrose and high fructose corn syrup, caramel…to Carbonated water, sucrose and/or high fructose corn syrup, caramel…to Carbonated water, high fructose corn syrup and/or sucrose, caramel…to finally Carbonated water, high fructose corn syrup, caramel…
In the meantime, New Coke went bye-bye.
As the formulation slowly changed, everyone became unable to tell the difference because the taste of 'Classic Coke' had been changed gradually instead of overnight...and New Coke was gone.
Then, when people get the chance to drink the Coke from Mexico, they immediately taste the difference and it's the USA-made Coke that has an odd 'feel' to it when compared to the sugar-based drink.