Is there a way to hook into the update-core page for custom messages?

by

There is an action, 'core_upgrade_preamble', which can be added to output anything you would like at the bottom of the upgrade-core page. For example, try:

add_action('core_upgrade_preamble', 'add_custom_upgrade_core_message');
function add_custom_upgrade_core_message(){
    echo "<p>HI THERE</p>";
}

That should work to meet your needs.