BuddyPress.org

Yes, enabling zlib compression by placing code in the header.php of a child theme will improve performance.

`<?php
ini_set(’zlib.output_compression’, ‘On’);
ini_set(’zlib.output_compression_level’, ‘1?);
?>`

Source: WPMU.org

Additionally, you could enable W3-Total Cache as a plugin and gain other benefits, ie. CDN, Minify, database caching, object caching, browser caching, and user agent groups.

https://wordpress.org/extend/plugins/w3-total-cache/

You cannot do both the plugin and the enabling of zlib compression in the header