Is it possible to tweak the theme so a user can change the variant selected in a drop-down by clicking the associated image thumbnail and vice-versa?

Absolutely! It was once a default functionality, however, Shopify requested we remove it because their research showed that thumbnails changing the active variant confused customers.

Instead of removing the functionality entirely, we simply moved it to an advanced setting and turned it 'off'.

All you have to do to turn it 'on' is make some edits to your theme code:

1. Sign into your Shopify admin
2. Go to 'Online Store' > 'Theme'
3. Click 'Actions' > 'Edit Code'
   
4. Scroll to the 'snippets' folder and select the 'settings.liquid' file
5. Convert