2002 Nissan Altima overheating

2002 Nissan Altima had overheating issue, taken to dealer and told thermostat and water pump were ok, tested system and found that coolant bypass hose was leaking. After repair (350.00) drove for 2 days and still had temp issues plus coolant boiling and leaking out of overflow tank. Advised that it was a head gasket issue and was adivised to replace head gasket (1800.00). Spoke with the service advisor after head gasket replaced and was advised that engine started and coolant was leaking out of the top of the radiator and was advised that flow pressure between the 2 chambers was uneven and was a sign of a clogged radiator and that it had to be replaced (350.00). I had seen no water in oil, white smoke out of exhaust or any other signs of blown head gasket. Could a leak in the head gasket cause overheating issues without oil and coolant mixing? Shouldn't the radiator have been checked before advising on replacing the head gasket?