No, however you should note the following points:
You may need to upgrade to the latest version of WorkgroupMail.
Installing IIS, if it is not already running, can impact the WorkgroupMail service since IIS comes with and runs, by default, its own SMTP service. If this runs it will conflict with the WorkgroupMail SMTP server. You will be able to receive, but not send, mail. The IIS SMTP service must be disabled. Please ensure that the IIS SMTP service is not running. Click Here for more information
The actual installation of WebMail will not impact the WorkgroupMail service.