Our vendor says it cannot be integrated.+
We check before accepting that answer. Many systems have an unadvertised way in, and if one is truly closed, almost all can still export on a schedule. If it genuinely is a dead end, we will say so plainly.
If one system updates, does the connection break?+
It can, which is why failure is made visible. A broken connection reports what failed and holds the pending rows so they can be replayed after a fix, with nothing lost quietly.
Which wins when two systems disagree?+
That is your decision, made before anything is connected. Each data type gets one system of record and the others follow. Without that rule, integration just spreads the disagreement faster.
How long does this usually take?+
What sets the timeline is not system count but how open each one is and how clear the data rules are. A system that exposes a way in moves quickly; a closed one takes longer because it has to go through file exchange.