Updating Plugins

I just got a notification through Update Notifications to update the domain mapping plugin.
I thought that it was possible to update this plugin automatically, because I entered my API key.
But I can only download an update, my question is, if I download the plugin, can I just remove the original plugin and replace it with the download? If so, does this not affect my current mapped domains? I cannot find any manual on this.

Thank you very much.