If I understand things correctly...the thermostat will not open until your car reaches operating temperature. So at first, you're just blowing air over a cold heater core. As long as that thermostat remains closed, and coolant isn't circulating, I suspect running the heater neither affects, nor is affected by, your engine temperature. Once that thermostat opens, though, and warmed coolant begins circulating, that's when you should have an exchange across the heater core, and that is the point where the heater being enabled becomes relevant..
In other words if you leave your car running in the driveway to get it warm, it should begin to heat up just as fast with or without the heat going...you don't need to make a second trip out to the car just to enable the heater. While it might reach the warmest temperature somewhat slower with your heater running from the start, I think the difference will be negligible. (You could always test it.. :)
As to your other observation, yes you can enable your heater in the summer if you are experiencing overheating, and it will provide a secondary/auxiliary heat dissipation surface. But you shouldn't rely on it. I only do this when I see my temperature begin to rise above normal. I'll enable my heater, and I'll give it about 30 seconds to a minute to make a positive effect. Thirty seconds to a minute, tops! Then, if the temperature continues to rise with the heater enabled, I pull over before I truly overheat! By the way...if applying the heater in this situation works and your temperature decreases, it signals an immediate need for some cooling system maintenance. In my case it's usually been a low coolant level, or possibly needing to "burp" the radiator.
Final thought. Contrary to your first statement:
I know that you should drive off immediately to warm up your car..
I believe it is better for your engine to allow it to reach operating temperature under idle conditions, as opposed to reaching operating temperature under load (driving conditions). When you start driving away cold, you're effectively putting very conditional, yet very avoidable, wear on several moving parts. If it were an airplane engine, taking off without a warm engine would be considered downright negligent...I'm just telling you that to underscore the performance relevance of a cold vs. a warmed engine. Obviously, the consequences of a cold automobile engine failing, or not performing as expected, are very different than those of an airplane.