responsive child theme to make existing site responsive

Someone has asked me to make their existing WP website responsive. They like the look and feel of their site and prefer not to change themes and redo it.

I’ve read that if I were to apply a WP child theme which is responsive and use the existing theme as the parent theme, but make no changes – simply apply the responsive child theme – that the site would look and function as it now does but would be responsive, because the child theme is responsive. Does this make sense?

Seems to me I’d still have to make css and potentially html changes to the child theme, or does the responsiveness of the child theme somehow supersede the non-responsiveness of the older parent theme?

Sorry for being so naive, much appreciate the advice.