That would be very difficult with the HTML5 responsive layout. It depends what layout you're using. If you want a side menu on the left you'll likely have to go with a fixed layout, or you'll need to really work at it to make it responsive with a lot of media queries in the CSS.
I'd say the PHP is not the problem, the templates can be changed all you want.. it's the template styles that would require a lot of work. If you look at alibaba, and resize it to 320 width, it can't manage that.
Something like
themes.tielabs.com/?theme=sokar
would be a theme like what you're looking for regarding the menu.. it would take a lot of work to integrate that into AbanteCart though.
You may be able to find a freelancer, etc. who could do that, but it's definitely not impossible.