Does WordPress cache get_user_meta() results?

Yes, it does. That function is a wrapper for get_metadata(). Inside of that you can find:

$meta_cache = wp_cache_get($object_id, $meta_type . '_meta');

if ( !$meta_cache ) {
    $meta_cache = update_meta_cache( $meta_type, array( $object_id ) );
    $meta_cache = $meta_cache[$object_id];
}