You cannot dynamically add a method to the stdClass and execute it in the normal fashion. However, there are a few things you can do.
In your first example, you're creating a closure. You can execute that closure by issuing the command:
$arr['my_method']('Argument')
You can create a stdClass object and assign a closure to one of its properties, but due to a syntax conflict, you cannot directly execute it. Instead, you would have to do something like:
$node = new stdClass();
$node->method = function($arg) { ... }
$func = $node->method;
$func('Argument');
Attempting
$node->method('Argument')
would generate an error, because no method "method" exists on a stdClass.
See this SO answer for some slick hackery using the magic method __call.