Can an integer be NaN in C++?

No, NaN is a floating point value.

Every possible value of an int is a number.

Edit

The standard says:

6.2.6.2 40) Some combinations of padding bits might generate trap representations, for example, if one padding bit is a parity bit. Regardless, no arithmetic operation on valid values can generate a trap representation other than as part of an exceptional condition such as an overflow, and this cannot occur with unsigned types.

So there may be some implementation specific invalid integer values, but there is no defined way to generate them.

Generally (and specifically in the case of C++, to the best of my knowledge): no.

Integer NaN

Most fixed sized integer formats do not have any way of explicitly indicating invalid data.

I think the most proper API to handle failures is to return a second integer error code in your api like:

int myfunc(args, int* realReturn);

The returned int is an error code.

The previous output is passed as a pointer in calling code:

int myInt;
if (myFunc(args, &myInt) != 0) {
//handle error
}