Does unit testing on Services make sense?

I am writing an app in Java Spring which consists of layers. The responsibilities of them are:

• REST/Controller layer - handle incoming requests, user authentification, parsing request bodies and communicating with Service layer according to the request
• Service layer - mostly deal with creating/editing/deleting associations between and states of Entities. Communicates with DAO layer and "Utility"
• DAO layer - persistence, will save/delete/find requested entities
• Entity/Object? layer - object representing the domain of the app, rather dumb functionality, mainly for keeping track of associations
• "Utility" layer - not really a layer, provides services like checking for permissions between objects (Object A wants to add object B to object C, for that it needs permission XYZ...) etc

I have been writing some tests while developing and now that I have thought about it, they have been kind of integration tests. The general flow of the tests can be described as:

1. Call serviceX to create object A
2. Call serviceX to create object B
3. Call serviceY to do something with objects A and B
4. Call serviceX to report state of objects A and B and check if everything is correct

In each step the services called the DAO layer and saved/created/fetched objects which were then manipulated and the test checked if the manipulation was successful and as expected.

I am thinking about how exactly should a proper unit test look. I understand that I should mock every component the tested service depends on so that I can 'isolate' the behavior I want to test. However, most of the methods of services do not actually "return" anything, they only manipulate the entities.

The question I have is then - does it always make sense to Unit test layers/services of an app, or is it acceptable to test them as a whole?

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Appendix

Example of one of the methods. This one is responsible for adding a new user to a group. Adding the member has to be done by a manager of the group. So the logic goes:

• Get parameters - manager, group, newUser
• If any of parameters are null, throw exception
• Call permissionHandler service and check if the manager user has enough permissions in group to complete this action
• Check if newUser already exists in the group. If yes, throw exception.
• If everything ok, call groupMemberHelper service to create a new GroupMember object representing the association between user and group (and some more info about the association)
• Add this GroupMember object to the group
• For all "items" the group already owns, call a helper service that creates a link between those items and the newly added user.

To test this method I would keep track of the group, newUser and all objects that this method affects and check if the state "before" and "after" are what I expect them to be.

I can't think of another way to test it without relying on the functions of the called services. Am I wrong?