javascript unassigned default function parameters

In the following function:

foo = function(a){
    if (!a) a = "Some value";
    // something done with a
    return a;
}

When "a" is not declared I want to assign a default value for use in the rest of the function, although "a" is a parameter name and not declared as "var a", is it a private variable of this function? It does not seem to appear as a global var after execution of the function, is this a standard (i.e. consistent) possible use?

It's a private variable within the function scope. it's 'invisible' in the global scope.
as for your code you better write like this

foo = function(a){
    if (typeof a =="undefined") a = "Some value";
    // something done with a
    return a;
}

because !a can be true for 0, an empty string '' or just null.

Yes, in this context a has a scope inside the function. You can even use it to override global variables for a local scope. So for example, you could do function ($){....}(JQuery); so you know that $ will always be a variable for the JQuery framework.

Parameters always have private function scope.

var a = 'Hi';
foo = function(a) {
    if (!a) a = "Some value";
        // something done with a
        return a;
    };
console.log(a); // Logs 'Hi'
console.log('Bye'); // Logs 'Bye'