Yes and no -- that's a flame sensor, but it's not the sort of flame sensor that occasionally requires cleaning.
The thing in the photo you showed is a thermocouple. It generates a small electric current when heated; that current serves to keep the gas flowing for the pilot light only. Because of their operating principle no cleaning is necessary. If the pilot remains lit then the thermocouple is working fine.
"Modern" furnaces have an ignition source at one side/end of the burner array and a flame sensor at the other end. The job of this flame sensor is to confirm that the ignition source has ignited the gas at the first burner and that the flame has traveled all the way across to the last burner. This kind of flame sensor is a stainless steel rod about the size of a 12 ga wire.
My experience with "older" furnaces, the vintage with a pilot light like yours as opposed to a spark or hot surface igniter system, is limited. It won't surprise me if your furnace actually does not have any other flame sensor apart from the thermocouple. Designers in that era may have presumed that if the thermocouple indicates the pilot is burning then it's safe to hold the main gas valve open.
If you can provide another photo or two of the entire burner area we'll be able to see whether yours has any additional flame sensor.
There's another component that could cause cyclic operation: an auto-reset high limit switch. This switch measures the temperature in the vicinity of the heat exchanger compartment. If that area gets too hot it'll interrupt the flow of gas. After it cools, which is aided by the blower continuing to run, then the gas can turn on again. If the high limit switch is tripping then you'll be well-advised to have somebody figure out why that's happening. It could be something as simple as a dirty filter or blocked registers impeding air flow, or a blower motor not running as fast as it should, or something more serious such as excess gas reaching the burner or possibly a leaking heat exchanger.