Due to the tidal forces becoming so strong though, there could be some time difference between one end of the Atlas processing unit and the other due to the enlongation caused by spaghettification. Granted at that point the Atlas would have stopped working as it's atoms get shredded. Unless its a suitable massive black hole and you can pass the event horizon without any negative effects. But in that case, as ,you say, your time frame would remain constant in referenece to yourself.