We do support GitLab on prem already, but right now it doesn't let you trigger deploy previews and branch deploys. Currently that's something we can help with on the custom plan, but we do hope to bring it to the normal tiers as well.
ping us in support and I can talk you through the setup w/the private repo (and branch deploys can be simulated with a few netlify sites attached to the same repo - no additional cost for additional sites on any plan)