Yes, you can use Acrolinx with Google Docs, Google Sheets, or Chrome.
There Are Two Ways of Deploying Acrolinx for Google Docs and Google Sheets
G Suite Admins use the add-ons in the marketplace for a 'Domain-Wide Installation' that is, an entire organization or groups within an organization. The Google add-ons for Docs and Sheets are available in the G Suite Marketplace.
The Acrolinx Apps are also available in the Chrome Web Store.* The Google Docs add-on in the Google Docs and Google Sheets add-ons each have their own product page in the Chrome Web Store.
Google deprecated the Chrome Web Store as of March 2019. You'll need to launch the Acrolinx App from the G Suite Marketplace.
Acrolinx is also available as a Chrome Browser extension. You can add the extension to your browser from the Acrolinx for Chrome page in the Chrome Web Store.