Other educators have pointed out that a lot of an organization's ability to change quickly depends on size, which is a major consideration when answering this question. There are also other factors to consider, such as the nature/funding requirements of the organization and the organization's work culture.
Some organizations, large or small, have stable funding through reliable profits, private investors, endowments, or other means. These are often for-profit organizations, though not always. Other organizations, such as many non-profits, rely on more short-term funding sources such as grants that must be re-applied for anywhere from every six months to five or ten years. There are also for-profit organizations that are just getting off the ground that might have variable or shorter-term funding sources. In organizations such as these, there may be an expectation that the work will change slightly depending on what the funders are looking for. While these aren't always structural changes, it is possible that an organization would need to apply for funding and go through huge shifts in organizational structure in order to get that funding. If an organization is already accustomed to making smaller changes, this might be able to happen more quickly than in an organization which is used to a stable funding source without changing outcome requirements.
Another factor to consider is both work culture and turnover rate. If there is a work culture where people have been doing the same job for a long time, it will take time to retrain them and get them accustomed to the new structure no matter the size of the organization. However, in a work culture where there is high turnover, such as in the food industry, it would be possible to make faster structural changes because new people are already being trained frequently.