If you disconnect the road from all services, they move out immediately. I just deleted all my residential roads and my population immediately dropped from 2.6 million to almost 0.
When I created all the roads again, my population was immediately around 1.6 million, and as happiness rose from about 10%, my population increased.
I think when my happiness was back to 55%, I had 2.3 million people. 100% is back to 2.6 million.
If you only have a problem with 1 service, it's only the excessive buildings that are affected, and not to a great degree if all other services are functional.