In my experience, the effectiveness of a weapon can be broken into four different categories. These are Ease of Construction, Lethality, Required Skill, and Usefulness, each being more important than the last (usually).
I think anyone who has every played Soul Caliber has thought about building one of these Whip-Swords, or maybe that was just me. Either way, it seems quite difficult. Normal swords aren't difficult to manufacture (we'll see what kind of debate that statement sparks) but they do require some level of skill. A truly exceptional blade would require a master smith to produce, but average blades can be made by less skilled craftsmen. Our whip-sword is likely going to require the master no matter what quality weapon we want.** The mechanisms inside the hilt that allow for the whip to be released (and retracted?) are going to be mildly complex, and the fastenings involved with the cord and the blade segments will require a fine touch. With practice this weapon may become easier to manufacture, though, and it would not be impossible, so if the weapon were truly superior to the easier-to-make weapons, it would be worth the time and effort, which brings me to my next point.
Most weapons kill or wound their targets, and the methods behind this vary greatly (arguably the most-studied thing in history!). As a sword, our whip-sword would be like any other but as a whip this weapon will either bludgeon/hack at the target or slice the target depending on the weight of each segment, the orientation of the blades, and the speed of the swing. Hacking and slicing are both pretty familiar, and both are fairly lethal in their own right. Hacking in particular is lethal, brutal, and effective, but slicing requires more finesse to be fatal, which brings us to the next category.
Here is where things get dicey. A weapon can be super lethal, but if no one knows how to properly use it the weapon will never be used. An excellent example of this in history is the crossbow vs. the longbow. Crossbows were inferior weapons by all rights, but they replaced longbows in many scenarios because the training required to become a proficient longbowman is extensive, while pretty much anyone can fire a crossbow. The whip-sword will likely require immense training to be a truly deadly weapon; much like nunchaku, an untrained person would likely hurt themselves or their allies rather than the enemy. Normally this would mean the weapon was impractical, but there are examples where this isn't the case. Longbows remained in service for quite some time because even though crossbows may have been easy to use, the longbow had many practical advantages over its competitor, like longer range and faster fire rates. And thus we come to the last point.
All of the above categories serve to support this final category. No matter how easy to make, lethal, and easy to use, if a weapon has only one single, specific application it will not be an effective weapon. Our whip-sword would seem to have two possible applications. The first is simply as a sword, and we know how those are useful already, though the whip-sword might be slightly less effective than a regular sword on account of the weakness of the joints between segments. The second is as a flail-type weapon. Depending on the length of the whip, the weapon might be useful at medium range. If the weapon allows the blade to be retracted back into a sword, these two applications might combine rather well, allowing the wielder to engage the enemy at longer range until they close at which point the enemy could be engaged with the sword. The whip would probably be dangerous and ineffective while fighting in a melee or in a battle line, but the sword function remains. It could also be effective on horseback, perhaps, though I shudder to imagine what would happen in imperfect conditions. What's truly important here, though, is that warfare is a famously fickle beast. The set of possible scenarios is probably uncountably infinite, and if someone were to think of a situation where the whip-sword were especially useful that could make a huge difference.
So where does that leave us? Compared to the sword, the whip-sword would be more difficult to make, about on par for lethality, far more difficult to use, and would be applicable in slightly more scenarios. But would it ever be used? That's debatable, but it definitely could be used, and I feel like that's the important part.
**You also asked when this weapon might be built. If we wanted the weapon to be able to retract back into a sword then I'd say probably the early Renaissance, though I'm no expert on such things. The metallurgy existed for the construction, chain or wire existed for the cord, and a simple release mechanism could be built using Roman-era technology. The retracting would require a spring, however, and coiled springs did not appear until the 15th century.