More on 98 Escort rough idle, and general car questions

I've done a lot more thinking about this rough idle problem on my 98 Escort, and I hope I'm closer to an answer. (By the way, the dealership wants to replace $250 of rubber mounting and insulating parts with an
additional $350 of labor. I don't think this diagnosis is consistent with the symptoms, and I'm damned if this problem is worth $600 to fix anyway, unless there is some actual functional issue lurking down the road).
Anyway, in the process, I've hit general knowledge deficiencies.
First general knowledge question: When a car is running, is the alternator capable of supplying *continuously* enough current to power everything in the vehicle? (Yes, I know it obviously must be putting out enough *averaged over time* to charge the battery as well as power the rest of the electrics. I'm asking if it is *continuous* or whether there are routinely spikes and dropouts that the battery is expected to fill).
Second: Is it possible for a battery to be "bad" (in some quantifiable way) but still be frisky enough to start the car immediately?
Here's what I've tested: There don't appear to be any vacuum leaks, at least none I can find by listening, feeling and dribbling water on the lines. However I also did the following:
1. Start car from cold (the problem doesn't happen - or not as bad anyway - when cold). 2. Turn steering hard over until the relief valve operates. Engine sounds like it's going to stall, the car vibrates, then everything smooths out. 3. Turn on rear defog element. RPMs drop then slowly rise ("staggers"), car starts to show rough symptom! Turn it off - smooths out again. 4. Turn on headlamps. Car starts to show rough symptom! Turn it off - smooths out again. 5. Wait for car to warm up. JUST BEFORE it starts to show the roughness, I hear a relay click somewhere. I'm guessing this is the radiator fan. 6. Drive around a bit, stopped at a red light, I hear the engine pulsing roughly in time with the turn signal.
Sooo... I think the "roughness" and vibration is simply very low RPMs resonating the body. I also think that the reason it happens more when warm is simply because the cooling fan is running. I also think my earlier experiment with the cabin temp. controls is a red herring - methinks it was the *fan switching on*, not the load on the vacuum system, that was causing the problem to show up.
So my thinking is an electrical problem. Perhaps the battery can't deliver enough current to power everything in the vehicle, so when I turn on an electrical accessory, the alt. is required to deliver more current -> loads the engine more. Is this line of thinking totally insane, or should I perhaps try replacing the battery (or is it more likely to be the alternator or a regulator module)?

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website by car enthusiasts for car enthusiasts. It is not affiliated with any of the car or spare part manufacturers or car dealers discussed here. All logos and trade names are the property of their respective owners.