No. A WorldShare user with the User Admin role can only assign the roles:
If a new or existing user needs access to a particular WorldShare module, the role can only be assigned by another user with the module's Admin role.
For example, WorldShare ILL roles can only be assigned by a user with the WorldShare ILL Admin role, cataloging roles for Record Manager can only be assigned by a user with the Cataloging Admin role, etc.
For a user to be able to assign every role in WorldShare, they need to have all of the Admin roles assigned to their user account.