As an Atlassian Connect vendor, it is possible to act on behalf of a user when a browser session is active.
It is not possible to do this for out of band requests, such as server-to-server operations.
This feature request tracks the ability for an add-on to request permission to act on behalf of a user. The user must explicitly grant this permission.
When granted, the add-on will be able to act on behalf of the user, restricted by the scopes that the add-on has.