I don't see why it wouldn't work with 1.5.7b, other than maybe requiring a careful merge of tpl_index_categories.php and tpl_index_default.php

As for the optional SQL query - it's optional. Copy/paste from the docs:
In case this automated installation fails for whatever reason, you can run the SQL patch manually.
So, unless for some reason the automated installer fails, there's no need to use the patch. As for the deletes - it would remove any previous database entries from this plugin, and then insert it again. Basically a (dirty) way of reinstalling - it doesn't check for existing entries and updates if necessary, but instead wipes any existing entries and inserts it back. Kinda like a factory reset...