yes, of course it is possible to do.
Here is the code to get all the categories on a page load, this code is prepared to go until the 3rd category generation.
$cats = get_categories( array('taxonomy' => 'product_cat', 'hide_empty' => true) );
foreach ($cats as $key => $cat):
if ($cat->parent == 0):
echo $cat->name;
foreach ($cats as $key => $cat2):
if ($cat2->parent == $cat->term_id):
echo $cat2->name;
foreach ($cats as $key => $cat3):
if ($cat3->parent == $cat2->term_id):
echo $cat3->name;
endif;
endforeach;
endif;
endforeach;
endif;
endforeach;