The typical answer is no. On any normal API call we will not log the data that was sent or received.
Some of the exceptions to this are formulas, bulk and events. On formulas, the data that is sent and received on API calls will be logged in the debug log. This data is stored for 3 days before it is deleted. However, if you are concerned about compliance, it is possible to turn off formula logging.
For Bulk, because bulk is an asynchronous job the data must be stored so that it can be downloaded when the job is done. Like formulas, this data is stored for three days before being deleted.
For events, the data received by polling and webhook events is stored in the event log.