No. In fact you only need to install it if you have users using desktop Outlook for their emails.
The app is only needed in you want to get the signatures written to desktop Outlook. If you use Outlook for on-premise Exchange, Office 365 or Google Apps for Work you also need it. THe same goes for Mac OS.
If you have users only using Outlook Web App for Office 365 or Gmail for Google Apps for Work, then you don't need to install anything on the client. You can deploy the email signatures directly from Xink.