Does Foxconn hourly workers need a resignation letter?

The specific situation depends on the content agreed by both parties. Generally speaking, there is no harm in avoiding saying nothing. The Labor Contract Law has the following provisions:

Article 69 Both parties to part-time employment may reach an oral agreement.

Article 7 1 Any party who works part-time may notify the other party to terminate the employment at any time. When the labor contract is terminated, the employer does not pay economic compensation to the employee.