Is it possible train an IntegratedML model on docker build or docker up?

Short answer, Yes. 

During docker build, just execute it, the same way, you doing anything when configure IRIS

While docker container starts, you can execute script, which will be called after start of IRIS

Just add it in the Dockerfile, trainmodel.sh, should contain iris session script to start model train

CMD ["-a", "/trainmodel.sh"]