trogau

You can query core, plugin, and themes individually, or check all at once.
It defines four new methods:
<ul>
<li>xmlrpcCoreUpdateCheck – checks core, returns true/false</li>
<li>xmlrpcPluginUpdateCheck – checks plugins, returns true/false</li>
<li>xmlrpcThemeUpdateCheck – checks themes, returns true/false</li>
<li>xmlrpcUpdatesCheck – checks all of the above, returns an array of trues/falses.</li>
</ul>
The plugin was created primarily for WPUpCheck (http://trog.qgl.org/wpupcheck/), a simple 
Windows application that remotely polls a WordPress site to see if updates are available.

XML-RPC Update Check

This plugin provides XML-RPC methods for checking the update status of WordPress websites.

Johan van der Wijk

This plugin disables all WordPress updates (core, plugins and themes). This can be useful if you have multiple environments such as a live and staging server and you don’t want your users to use the update functionality.
This plugin not only disables the update mechanism for the core, plugins and themes, but it also removes the update menu item from the left navigation menu in the admin dashboard.

Disable Updates for WordPress Core, Plugins and Themes

Disables the WordPress update checking and notification system for all core, plugin and theme updates.

XML-RPC Update Check vs Disable Updates for WordPress Core, Plugins and Themes