In the movie Focus, you can find this scene, where a man puts on a neck brace, before crashing into another car, and this same guy seems to be the only one unscathed. I know movies tend to portray crazy stuff but, would doing that in real life make a difference?
It's hard to say whether something like a cervical neck support brace would actually protect you it a high velocity collision. Such a device is normally meant to support your neck from existing injury worsening, based primarily on preventing overuse, over-extension, or over-flexion. They are meant to hold up the weight of your head and that's about it, not the weight of your head at 100 miles per hour. This seems a common knowledge issue to me but the Wikipedia article on cervical collars is well-sourced for their purpose.
However, in stock car racing they have requirements for a HANS device (head and neck support). In NASCAR it includes a specially engineered harness that wraps around the head and down the shoulders. The driver wears a helmet and is tethered by the head to the harness. The item appears far more restrictive and protective than a simple neck brace. Yes, the stock cars are racing much much faster than a typical collision would occur at, but that doesn't change the fact that neck braces are not designed to withstand or protect against high velocity rapid deceleration. And devices that are designed to protect against rapid deceleration, like the HANS device, are far more restrictive.
In researching the beneficial effects of wearing a neck brace for motorcycle riders Dirt Rider magazine put out a very well referenced article in 2013. Though not quite the same thing they conclude:
From my experience touring the Leatt laboratory, and my research since then, including discussions with employees at Alpinestars and Atlas, the evidence available today leans heavily in favor of wearing a neck brace. In fact, not a single expert I spoke with (doctors and biomedical engineers) discouraged wearing a brace.
But again, I should stress that those neck braces are designed to protect against motorcycle crashes, whereas the cervical neck support brace is designed merely to support your own head from the force of gravity only. Simple observation of the design differences and material specifications indicate this. I think you are right to be skeptical that a cervical neck support brace would provide any marginal protection in a high velocity collision.
An interesting meta issue is that wearing the neck brace may make you more likely to cause a collision, therefore, may increase your liklihood of injury. NCBI reports that wearing a brace while driving affects driver performance.