The short answer is: no, not really.
The long answer is that the giosg script tag is asynchronous and doesn't have much impact on the initial rendering speed of your website. Asynchronous means that the giosg script tag writes another script to your website and starts loading scripts in parallel with
other resources of the page, so that loading the relevant materials from our servers won't block the rendering of the page.
Only customer specific settings need to be downloaded for every page load. Other resources and scripts that the giosg system uses are heavily cached until a new version is released from giosg. This means that if a visitor has visited any other website containing the giosg script before visiting your site, they will already have all the relevant scripts on their browser's cache (except for customer specific settings).
The relevant resources are also compressed using gzip to minimize bandwidth usage. Javascript and CSS files are also minified. For very slow mobile connections downloading the giosg scripts in parallel with actual page may slow down page loading, but this is
not notable for majority of mobile users. Usually there are other factors that affect the website's speed more than the giosg script and chat.