Chip, you appear to be correct. I switched back to the default WP theme and there are no post images or thumbnails displayed. In fact, it appears that a theme needs to support WordPress’s new “Featured Image” functionality, which the Thesis Theme currently does not by default.
However, adding:
add_theme_support( 'post-thumbnails' );
to the theme’s custom_functions.php file enabled Featured Image support and now everything works like I want it to. WPTouch now displays Post Thumnbnails for every post for which a featured image is set.