Pro/con: Initializing a variable in a conditional statement

The important thing is that a declaration in C++ is not an expression.

bool a = (CThing* pThing = GetThing()); // not legit!!

You can't do both a declaration and boolean logic in an if statement, C++ language spec specifically allows either an expression or a declaration.

if(A *a = new A)
{
    // this is legit and a is scoped here
}

How can we know whether a is defined between one term and another in an expression?

if((A *a = new A) && a->test())
{
    // was a really declared before a->test?
}

Bite the bullet and use an internal if. The scope rules are useful and your logic is explicit:

if (CThing* pThing = GetThing())
{
    if(pThing->IsReallySomeThing())
    {
    }
}

About the advantages:

It's always recommended to define variables when you first need them, not a line before. This is for improved readability of your code, since one can tell what CThing is without scrolling and searching where it was defined.

Also reducing scope to a loop/if block, causes the variable to be unreferenced after the execution of the code block, which makes it a candidate for Garbage Collection (if the language supports this feature).

You can have initialization statements inside if and switch since C++17.

Your code would now be:

if (CThing* pThing = GetThing(); pThing->IsReallySomeThing())
{
    // use pThing here
}
// pThing is out of scope here

if (CThing* pThing = GetThing())

It is bad style, because inside the if you are not providing a boolean expression. You are providing a CThing*.

CThing* pThing = GetThing();
if (pThing != NULL)

This is good style.