No, a noisy fan is not necessarily a sign of CPU failure. A fan can become noisy for a variety of reasons, some of which have nothing to do with the CPU.
First, it is important to understand what purpose a fan serves in a PC. Fans are used in computers to help dissipate heat from components and keep them from overheating. Typically, a CPU will generate the most heat inside a computer and thus require the most cooling. Other components such as the graphics card and hard drive can also generate heat, so are also cooled by fans.
When a fan becomes noisy, it is usually a sign that something is wrong. There are several possible causes of a noisy fan, however, only one of which is related to a failing CPU. The most common cause of a noisy fan is dust buildup. Over time, dust can accumulate on the fan blades and in the vents of the PC, reducing its effectiveness at cooling the components. As the fan struggles to spin to move the air, it can start to make more noise. Cleaning the fan and vents of the PC can usually fix this issue.
Another common cause of a noisy fan is that the fan itself is failing. Since fans are mechanical components, they can wear down over time and eventually stop working. This usually results in an increase in noise as the fan spins faster and faster in an effort to cool the components. Replacing the fan should solve this problem.
A third cause of a noisy fan is a failing power supply. The power supply is responsible for providing the electrical power for all components in the PC. If the power supply is failing, it may not be able to provide enough power, resulting in the fan spinning faster and making more noise. Replacing the power supply should solve this issue.
The final, and least common, cause of a noisy fan is a failing CPU. CPUs can fail for a variety of reasons, such as age or damage from an excessive voltage spike. When a CPU fails, it will often draw too much power, causing the fan to spin faster and make more noise. In this case, the only solution is to replace the CPU.
So, while a noisy fan can sometimes be a sign of a failing CPU, it is far more likely that the fan is making noise due to another issue such as dust buildup, a failing fan, or a failing power supply. Before assuming that a CPU is failing, it is important to rule out all other possible causes.