Unfortunately, there isn’t a way to do that. What would be ideal, is if it raised a banner notifying the artists that there was an update available.
If your artists use SG Create instead of SG Desktop to launch the integrations then it will load the latest config every time they try to show the open in actions on a task.
Are you using distributed configs or an installed centralized one? If you are using distributed configs you can set launch_builtin_plugins: [basic] as an engine parameter in the env settings. Doing this will mean that the engine uses its plugin-based startup rather than the older classic based startup. This means that when you launch Maya from Desktop, as part of the Maya Shotgun bootstrap processs it will download the relevant up to date config.
This obviously won’t affect Desktop, that will continue using the older config until the user back out of the project and back in, but it will mean that the launch DCC should be using the latest.
I should note not all engines have this parameter, only the ones that work with the basic config I believe.
I’ve pinged the product team with a suggestion to improve this behaviour.