Programmatically export a UV Layout

Is there a method to programmatically export (from Python script) a UV Layout?

Since there is a plugin which does the job, is it possible to programmatically activate the plugin?

I assume the addon you refer to provides a button or menu entry to do so, which means you can call the underlaying operator with a script as well. You may need to switch the context area type to UV editor however and possible switch mode for a proper execution context.