Hi Remy.

It is not included in the After Start Checklist because it's in the Before Takeoff Checklist. I don't think it could hurt to turn it off after starting the engines though.

From the ‘707 Captain’ FLIGHT MANUAL Part III – Normal Procedures, page 27:

AMPLIFIED BEFORE TAKEOFF CHECKLIST
After leaving the gate and prior to taking the runway, the Captain will call for the Before Takeoff Checklist.
The Flight Engineer will read aloud each challenge and receive the appropriate response from the designated
crew member.
Nacelle Anti-Ice OFF/ON F/O
Check nacelle anti-ice valves positioned OFF or ON as required.
Attitude Warning CHECKED F/O
Ground Start Switch OFF F/O
Window Heat HIGH F/O
Check window heat switches on HIGH and OVERHEAT lights extinguished.
Probe Heaters ON F/O
Check probe heater switches ON and HEAT ON lights illuminated.
Fit Dir, Fit Inst and Radios SET FOR DEPARTURE C,F/O
Speedbrake Lever FULL FORWARD С
Flaps 14, 14, GREEN LIGHTS С
Check both flap position indicators indicate 14 and green LE FLAP lights illuminated.
Start Levers IDLE DETENT С
Stabilizer Trim UNITS С
Check stabilizer trim setting agrees with computed setting.

Mark