This dependsd on the carrier. For example, if you were to buy a stolen ATT branded cell phone they would not know since they do not blacklist IMEI numbers that are present on the phones. There is no 'activation' for using ATT phones if you have a currently active SIM & account that is not past due. OTOH, I know Verizon does add stolen/lost handsets to their list which prevents it from being activated on someone else's account. Not sure about the other CDMA carriers.
If someone were to sell me a lost or stolen phone, would it be identifiable through the cellular carrier i activate it with?