Is it safe to use a laptop if the CPU fan is failing?

Will it work? Sure. Is it "safe"? Maybe

Modern CPUs, especially mobile ones, feature thermal throttling in order to protect them from extreme temperatures. What this means is that if a fan fails while the system is in operation then the CPU will limit itself in order to prevent damage caused by overheating. Your system performance can be severely hampered by this throttling.

While this can ensure that a system is likely to be protected from a failure you shouldn't count on it as a permanent saviour. Electronic components don't like being at their maximum limits for extended periods. Extreme hot/cold cycles can cause mechanical stress and lead to components breaking prematurely.

The fan heatsink may be connected to the CPU, but by keeping the CPU cool it also allows other components (such as power converters and interface chips) to shed heat easier.

I would only use such a system lightly and with caution. It will not be working at peak performance and will be at risk of further damage due to high temperatures around sensitive components.

No, this is not safe. Stop using your computer right now.

Maybe, just maybe, the CPU will protect itself from immediate death by thermal throttling or emergency shutdown.

However, the fan in a laptop does not only cool the CPU, it also cools other components in the system. Anything in your system may break including irreparable damages to main board, memory, or your disk and thus permanent loss of data. Even a emergency thermal shutdown can easily corrupt your data or file system.

If you value your hardware or data, you should not use the system until it is properly cooled again.