My general advice is to do integration testing after push.
You say that you value the testing harness having the same set of dependencies as your deployable artifact. With GCCB, you are not limited to one image with your build - it can be any number of them.
So, something like
1. build the deployable as gcr.io/project/service:${REVISION_ID}
2. build the testing harness as gcr.io/project/testing:${REVISION_ID}
3. build the db container as gcr.io/project/db:${REVISION_ID}
Then, you can spin up a test environment using the ${REVISION_ID} tags, and do your integration testing there with the same nice guarantees.
That all said, it's certainly possible to do fancier things within the build itself. Using the gcr.io/cloud-builders/docker build step, you can run any docker command. We haven't seen the need to directly support a docker-compose build step, but making it would be easy (different entrypoint on the docker build step) and it would automatically connect to the worker host's daemon.
You can also run several of these docker build steps in parallel, or run one that does 'docker run --name=foo -d ...' and have the others run with '--link foo:foo', etc.
We try not to limit the sorts of things you can do, and provide bonus features like the docker daemon's socket, service account credentials etc.
You don't even need to build a container image, if you don't want to. Just provide some container images and we'll run them for you, pipe the logs back to you, and let you know how it went.