This would not work in the real world, let me explain.
Physics dictate that when you release the string of the bow, the energy stored in the bended limbs of the bow is transferred to the arrow, the bow limbs and the bowstring.
Because of this, the relative weight of the bowstring and bow limbs, is very important: the heavier the bowstring and bow limbs in relation to the arrow, the less energy is left to transfer onto the arrow (because a larger part of the energy stored in the bend limbs is needed to move the string and limbs).
In other words, a bow needs light weight limbs (especially near the tips) and a light weight bowstring. The light bowstring is not hard to achieve with modern materials, as long as it is made in one piece. Any type of 'connector' would severely hamper you bow's performance. Light limbs are perfectly possible too of course, if you don't include the requirement that the limbs should double as a sword/saber/scimitar.
The image on the URL liked in the OP shows saber (or scimitar) shaped blades. Any flexibility / bendiness in swords or sabers is perpendicular to the width of the blade. So, in order to use the blade of your sword as a bow limb, you would need a symmetrical (non-curved) blade (or otherwise, your bow would swing/turn in your hand as soon as you start pulling a string attached to the tips of your blade). This means that the saber/scimitar shape has to be replaced by a straight bladed sword.
For our blade to double as a bow limb, we would need it to be quite flexible. A flexible blade would be quite useless for stabbing, so instead we would have our blade rely on slashing/cutting to wound our opponent. 477
However, a cutting sword relies, in part, on the weight of the weapon to do damage. The lighter the blade, the less of an impact it would make when hitting our opponent. And there lies the contradiction: for an effective cutting weapon, your blade needs a certain minimum weight, while an effective bow limb needs to be as light as possible.
Even if you made two symmetrical, straight, flexible bladed swords, joined them together at the handle (joining two bow limbs at the handle is commonly done with take-down bows, so this should not pose a problem) and attached a string to the end of one of the two blades, you would be faced with the part of stringing your bow.
This could certainly be done, but it will takes a bit of time and is certainly not something you quickly do in a combat situation. If the bow has a low draw weight, it can be done in a couple of seconds (but at low draw weight bow is useless for combat). Stringing a heavy draw weight bow takes more time and quite some effort. Stringing a bow with sword sharp edges would take quite an effort and require the absolute care not to cut yourself, when building up tension on the bow limbs/the sword blades.
So, while I can see the cool factor for in an anime, it is not really an option in the real world. If you wanted to make a non-functional prop (for cosplay or something) you could probably makes something that looks ok, but it would not be a functional weapon. At the very best it would be a combination of a weapon that is hampered in its primary functioning by a non-effective secondary idea.
For any practical use, having either a bow or a sword would be better. Having both a sword and a bow would be the given solution for having both. 523