It appears your code will do the opposite of what you want, it should display the thumbnail. To test this, just temporarily add some text to the "if" statement...
{if $cat != '126'|| $manufacturers[id].manufacturer == '0' }
TEST
<a href="{$url}">{include file="product_thumbnail.tpl" productid=$product.productid image_x=$product.tmbn_x image_y=$product.tmbn_y product=$product.product tmbn_url=$product.tmbn_url}</a>
{/if}