Other than specifically coding with WorkerThreads (which it doesn't sound like you are using), nodejs runs your Javascript code in only a single thread (e.g. the interpreter itself just uses one thread to run Javascript opcodes).
But, nodejs does have other threads that are used in the implementation of library functions such as file system operations and crypto operations and for the garbage collector. And, some 3rd party libraries may use native threads in their own implementation. So, it is definitely possible for nodejs to use more than just one core. It really depends upon what the code/task is doing and what library functions are being called.
Is it possible that the workload could take up the whole CPU so it moves some of the load to another CPU?
It does not move the running of your Javascript to another CPU. But as I said above, some library functions that use native code may use additional threads.