How does automatic memory allocation actually work in C++?

Question

In C++, assuming no optimization, do the following two programs end up with the same memory allocation machine code?

int main()
{     
    int i;
    int *p;         


        

Answer 1

No, without optimization ...

int main() 
{      
    int i; 
    int *p; 
}

does almost nothing - just a couple of instructions to adjust the stack pointer, but

int main() 
{ 
    int *p = new int; 
    delete p; 
}

allocates a block of memory on heap and then frees it, that's a whole lot of work (I'm serious here - heap allocation is not a trivial operation).