I think the point here was that if the river uncovers bedrock, then it will try very hard to go around. If that bedrock is at the mouth of a large valley that's recently (in geologic time) had an uplift, then your scenario is reasonable to a certain point.
A river's gradient profile (steepness over its course) tends to look suspiciously like the positive half of a 1/x function. That is, it starts out steeply in the mountains and becomes essentially flat in its lower reaches for long rivers. The energy of the flowing water in the almost-flat sections goes into side-to-side cutting, making meanders. The gradient also tells you the kinds of things that the river can carry. A steeper gradient lets the river carry larger sediments. For a large river near its mouth, it's carrying little more than very fine clay and dissolved materials. The rest has settled out upstream. One of the reasons why a river tends toward near flatness in its lower reaches is because the dropped sediment becomes new land. Floods raise the river level and increase its power to carry larger sediments. These sediments are carried off to the sides of the river when it overflows its banks, forming natural levees (and when the river hits the completely-flat ocean, it drops anything that's not dissolved pretty rapidly).
If the gradient of the lower part of a river is made steeper by uplift, then the river will start cutting down until it can be as flat as possible. It sounds like this is the sort of thing that you're looking for.
If the river's course is narrowed for whatever reason (landslide, log jam, or what have you), then the river will become more turbulent, which increases its cutting power. Islands in a river are unlikely to appear; if they do, the river will use that extra energy to cut its banks out just as quickly as it can to restore its flow.
Having channels that go around rapids on a lake usually involves a lock system, and for good reason. Without the locks, the bypass channel will be at least as steep as the main river channel, and likely steeper. The river will want to flow down the steeper channel, meaning that the new bypass channel and ponds will eventually capture the main river unless careful steps are taken.
Ancient Portus on the Tiber River is analogous to what you're asking about, I think. The engineers dug out a large harbor, but the reason was more about having a better harbor than bypassing a river, even though there were bypass channels in place. I'm not sure how well it would have worked if the river had been relatively swift-moving at that point.