Would chaos ensue? Probably not. But organizations often do struggle when key leaders, staff members, or other professionals are lost. Does it have to be that way?
One of the primary objectives of management is to ensure continuity of service and long-term sustainability of the business. This is accomplished by establishing a sound quality management system that requires disciplined thought and action from all leaders. One of the prescribed requirements is a resource contingency plan.
A resource contingency plan identifies those roles within the organization (including yours) that are essential to business continuity and/or product quality. It should outline both the short-term and long-term replacement strategy if/when the resource becomes unavailable (planned or unplanned). It can also be used to drive employee development efforts and succession planning. A well thought out resource contingency plan allows the organization to sustain the desired levels of performance even when critical human talent and intellect are lost.
So, how would you answer the original question? We should take no pride in knowing that the business would suffer without us, whether true or not. The greatest satisfaction comes when you know that your efforts have created an enduring legacy for future generations of the company. It may seem counter intuitive, but if your company lost you tomorrow, one of the best indicators of your management prowess would be how well they carried on without you.