If it is a Rochester, then it will be a Quadrajet. It uses mechanical secondaries, with an Air Valve. The secondary throttle after is connected to the primary shaft through a spring loaded linkage, where the secondary shaft is locked from rotating while the choke is on. Once the choke opens fully, the interlock is released and the secondaries will open now as the shaft can now rotate. The secondaries will open fully when the throttle shoved all the way to fast, irregardless of the engine rpm. Little air flows through the secondaries until the engine speeds up enough for the proper pressure difference on the secondary air valve to open slightly, riding on a cam that turns as the air valve opens is a hanger connected to the fuel metering rods for the secondaries. the more the air valve opens, the higher the metering rods are raised. You may have something holding the secondaries open the slightest bit at idle, but becauae manifold vacuum is high when the throttle is at idle, enough air can get past the air valve-carb body to cause issues, especially the if the choke pulloff/airvalve damper is leaking or not connected to manifold vacumm. However, I would also be looking for any vacuum hose, either disconnected or leaking, Marine carbs are generally richer than auto carbs so an air leak might not show as a rough idle.
It is possible the auto choke is cooling off and raising the fast idle linkage enough to speed the motor up
