Doesn’t appear to. Apparently QuickEdit does not use the "rank" field in the site_tmplvar_templates table. It most likely just loads in the order they are in the table. It shouldn’t be difficult to add a "order by" clause to the query it uses to retrieve them, though.
Looks like line 141 of assets/modules/quick_edit/contentVariable.class.inc.php is the culprit...
$templates = $modx->db->select('templatename,id', '`' . $modx->db->config['table_prefix'] . 'site_templates`','','rank');
should do the job, although I haven’t tested this.
[edit] That will only break your pages when QuickEdit is activated. There is another (proper) fix; I can’t find the post with it again though!
On line 167 of output.class.inc.php it should be (the last parameter indicates ORDER BY field)
$cvs = $modx->getTemplateVars('*', 'id, name', '', 1, 'rank');
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