Hi Sam,
When you say Webex chat I am making an assumption that you are referring to "Webex" formally known as "Webex Teams".
Under most circumstances no, an administrator can not view Webex (Teams) messages for an individual user. However, there is a eDiscovery feature which could be used to export the data of particular conversations. The Admin would need to be granted the "Compliance" officer role by another admin to perform this function, and these exports are also logged in the control hub audit log. Further reading on this function here: https://help.webex.com/en-us/nr70c1m/Ensure-Regulatory-Compliance-of-Webex-App-and-Meetings-Content
Users should take care to realize that their messages can be read using compliance tools. This is a corporate messaging platform and users should be aware that their messages are essentially the property of the company (no expectation of privacy) and could be read without their knowledge by a user with the compliance officer role at any time (as bad as that sounds).
