So, for the argument's sake, let us just assume that all of the workers in this planet simultaneously stop their work. What would happen? If all productions stop, I assume that most businesses (especially those which use employee/employer system) will also stop save for businesses that are being run by individuals. My assumption that individual businesses will still conduct their business activities is based on two further assumptions: (i) they are their own masters, and therefore, there is no need for them to follow the workers, and (ii) they can run their businesses without significant dependance on other businesses or infrastructure support. In short, they would be most likely local businessmen who have the capacity to produce their own products by themselves.
Now, you can always stop working, but you can't stop living. You still need to obtain your basic needs right? If you can gather everything by yourself from the nature, that would be fine. But if not, what would happen? You'll depend on other people, and in this case, you will depend on the above individual businesses during your strikes while waiting for the crumble of capitalism.
In such case, the law of supply and demand will automatically work. With less supply and more demand, price will increase. Even worse, without any competitors, the local businesses will eventually have enough monopoly power to solely control the price of their goods and services. And trust me, that would be a very bad scenario.
Let me give you an example: previously a local farmer sells an apple for US$2. In reality, he's almost out of the business since he can't compete with the local supermarkets which are far more efficient than him and can sell their apples for US$1 each. But, with the great labor strike, the supermarkets cease to operate and the farmer becomes the only apple seller in the community. Imagine his power now to determine the price of his apple without any competitors. Why bother charging US$2 if you can get a higher price? After all, people can only get apples from you.
How about the workers? Without a job, the only thing that they can do is to use their savings, or they can try to become businessmen on their own, selling their own services/products to other parties. If they can do it, that would be nice, if not, they will need to rely on the new capitalists, i.e. the individual businessmen as I described above and the cycle will begin again. The irony is: in order to survive, they need to become new capitalists.
So in the end, at best, the strike will only produce new capitalists and a new cycle of capitalism. At worst, the workers lose their savings before the rich guys lose all of their money and therefore, the old capitalism prevails. In any case, it won't change the fact that servants and masters will always exist.
The problem lies with human nature, namely: the basic needs for surviving in this world. In the past, in order to survive, men must have a lot of skills. In such case, only the true elites can survive while others perished. But humans are not stupid, there is an easier way to survive, and that is by interacting and cooperating with others.
Unfortunately, by default, you can't get anything for free. Either you need to obtain your needs by self labor (producing everything by yourself) or you exchange something with others to obtain what you need from them. This process creates the market and within such process, the iron law of supply and demand will eventually lead some people to be on the top place while others will stay below depending on their skills and luck.
The above analysis is made on the assumption that order and authority remain to exist. But how about in worst case scenario when there is a revolution? Suppose the workers are out of their savings and they decide that they will take control of the resources from the businessmen. Will that change the analysis?
My answer is no. Once the workers gain control of the resources, similar issue will still exist. Even if you have all the money in the world, you can't do everything by yourself. Some will still be better at doing things than you and the process of exchange of products and services will start again. This will lead to another cycle of supply and demand, market, etc. And before you know it, capitalism will return swiftly. Of course, this is also assuming that those workers will distribute the resources evenly in the first place. If not, even from the very beginning, new masters will emerge without having to wait for another cycle of capitalism.
In the end, I don't think the slogan "All Workers Unite" will work to end capitalism. It will just produce another capitalism (but with different "capitalists"). It is still a nice slogan though, has a nice ring to it, and sounds powerful. Well, at least it is perfect for campaign and propaganda.