I'm by using this little bit of code to create custom publish typess show on my small category pages:

<?php $paged = (get_query_var('paged')) ? get_query_var('paged') : 1; query_posts(array( 'post_type' => 've_products', // custom post type 'paged'=>$paged, )); ?>

It is possible to way I'm able to modify this code to incorporate it into functions.php rather than category.php and get exactly the same effect?

Thanks!

You need to have the ability to give a posts_where filter to offer the same effect, something similar to this:

function ve_products_sql_where_clause($sql) {
  if (is_category()) {
    $sql = str_replace("wp_posts.post_type = 'post'", "wp_posts.post_type = 've_products'", $sql); 
  }
  return $sql;
}
add_filter('posts_where', 've_products_sql_where_clause');