Is include()/require() with "side effects" a bad practice?

Yes, IMHO it's (very) bad practice unless very explicitly documented.

include or require (and their equivalents in other languages) should normally only introduce new functions into the current scope, and never trigger their invocation.

That's a question of general design, not personal preference. If you can design with personal preference, then it's your personal preference. Do whatever you like, use the language as a tool.

For example, if you use PHP as a replacement for server-side includes, it's pretty common that includes contain mostly HTML with some PHP fragments. Great sites were built with this. There is nothing bad with that kind of design in the real-world.

However if you need more fine-grained control you're mostly referring to objects instead of files. In that case I suggest you shouldn't have any include in your code, but an autoloader that requires as needed upon request by classname in your application.

The example you have in your question however looks like that there is not much concept behind it anyway, maybe it should allow having local variables inside an include, however that can be more easily achieved by including dynamically inside an include helper function like:

/**
 * include a file with it's own local scope.
 * 
 * @param string path to include file
 * @param array (optional) variables, keyed with variable name.
 * @return mixed return value of include
 */
function include_helper()
{
    if (!func_num_args())
    {
        return NULL;
    }
    elseif (2 === func_num_args() && is_array(func_get_arg(1)))
    {
        extract(func_get_arg(1));
    }
    return include(func_get_arg(0));
}

And therefore spare to define a function inside each include having the same name as the include.