You won't need any alters. Just go to the template in which you want to place the registration form and add,
$form = drupal_get_form('user_register_form'); print drupal_render($form);
This will print the user registration form. It's always good to have a check for anonymous users as a wrapper of this output.
Edit #1 (After question update and comments) I suppose you want to create a block that will appear in your "admin/structure/block" page and you can assign the block in any desired region? - Right? I don't think your question says the same but this can be done in the following way,
- Create a hook_block_info() & hook_block_view()
- In the hook_block_view() assign the "content" the following,
$form = drupal_get_form('user_register_form'); $block['content'] = drupal_render($form);
I hope this can solve your problem. I haven't tested this yet!