This problem was two fold.

The first is that I was not returning the promise event (the $http call).  The lack of a return statement (as @tobo points out) is what was causing the error directly.  I needed to be returning the promise though, not the array.

The second is that I need to be using .then rather than .success for AngularUI-Bootstrap to pick up the results.

I ran across the following question:
How to tie angular-ui&#39;s typeahead with a server via $http for server side optimization?

Which updated my function call to the below:

$scope.getTypeaheadValues = function($viewValue)
{
    return $http({
        method: 'GET',
        url: 'api/v1/person?name__icontains=' + $viewValue
    }).then(function ($response) {
        var output = [];

        console.log($data);

        $response.data.objects.forEach(function (person)
        {
            output.push(person.name);
        });

        console.log(output);
        return output;
    });
}


AngularUI-Bootstrap's Typeahead Can't Read `length` Property of `undefined`
Obviously I know the answer is yes, but if I visited a European country and stole something there would I actually be put in jail and face trial or be deported or face trial in the US? 
