No, both method(1) and method(new Integer("1")) will cause the error, but it never makes it to evaluating either of these statements, as the compiler fails simply parsing the method declarations. It hasn't even gotten to evaluating what is inside the methods.
Please continue the discussion in the original thread.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus