Yes: Since there is no official “development server” for Serverless Framework I did not expect the sls offline to work very well but it did. So we can write and run both unit tests and integration tests locally and in our GitLab code pipeline.
I thought that the environment of AWS Lambda was too complex to reproduce locally and that a community effort could not do it. But it works! And it is a big difference for trying out small changes locally instead of the alternative of deploying and debugging the Lambda functions in the AWS cloud.