Yes, you should remove or comment out the block of code in skin1/customer/main/subcategories.tpl
Code:
{if $subcategories}
<table cellspacing="5" width="100%">
{foreach from=$subcategories item=subcat}
<tr>
{if $tmp and $first_subcat ne "Y"}
<td valign="top" rowspan="{count value=$subcategories print="Y"}"><img src="{if $current_category.icon_url}{$current_category.icon_url}{else}{$xcart_web_dir}/image.php?id={$cat}&type=C{/if}" alt="" /></td>
{assign var="first_subcat" value="Y"}
{/if}
<td class="SubcatTitle"><a href="home.php?cat={ $subcat.categoryid }"><font class="ItemsList">{ $subcat.category|escape }</font></a><br /></td>
<td class="SubcatInfo">{if $config.Appearance.count_products eq "Y"}
{if $subcat.product_count}{ $subcat.product_count } {$lng.lbl_products}
{elseif $subcat.subcategory_count}{ $subcat.subcategory_count } {$lng.lbl_categories|lower}
{/if}
{/if}</td>
</tr>
{/foreach}
</table>
{/if}