I don’t see why it wouldn’t be possible. I use a switch plugin to display a totally different theme for mobile. A child theme is a totally different theme. The dependencies on the parent theme should still work, as they are WP functions built in.
Give it a try with a super simple child theme so you don’t waste too much time. Just set up the style.css, use the import rule, but do something simple and drastic like changing a really obvious colour. See if it works.