Inspect the source code for the admin control panel (administrator/index.php). There is an empty div that previously contained the postinstall messages.
Apply the patch.
Inspect the source code again. The empty div should be gone.
Reset the postinstall messages to display them again in the control panel.
Make sure the messages are still displayed correctly.
Attribution
This issue and the corresponding fix have been reported / proposed by user Cartho on joomla-bugs.de (Original Thread).
Looks fine from review and makes sense.
Can you maybe adjust the indent of the inner HTML block? Since you remove an if clause.