Is there any way to query user activity for those that have access to SumoLogic?

Yes, you can do that, using functionality called "Audit Index". Using the audit index you can see the record of the user's different activity in Sumo Logic.

For more info please use below link: User Activity Events

Below is the query which you can use to get some user activity:

_index=sumologic_audit _sourceCategory=user_activity

Note: Only the users who have "Administrator" access can access the Audit index.