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I to coast my car A LOT with engine shut off. The car is a 40 year old Saab 96 V4 with a simple DIY relay box and two buttons on the shift stick - one for stopping the engine by interrupting the ignition and holding it that way, the other for cranking the engine and restoring power to the ignition coil. There's no electronics at all in this car so I guess there may be a few amps for the ignition in average to keep the engine running, and that's all.
In Sweden we have a law that forces you to have headlights, foglights or similar always lit, even in full daylight. (the tail lights can be off until it's starting to get dark) I have installed LED-lamps in the tail lights AND 4x1W white LED's as a compromise replacement for the front parking lights. This is about equal to the minimum daylight lights we must have in daytime on an older car and is save's A LOT of my battery while coasting about 2/3 of total driving time. That one third to half of total driving time my engine is running is offcourse splitted into many many cycles of perhaps only 15-20 seconds of acceleration.
From what I know, a lead-acid battery takes some time to reverse the chemistry and start charging after current is applied. I don't know how long this time actually is, but I have heard this is one major reason against regenerative breaking with lead-acid batteries in an EV. This leaves even less time for the alternator to charge my battery, but in some magical way the equation isn't too bad in the end. Most of my travels are done in about one hour and I always have power enough the following days to start my engine. Oh, I almost forgot to tell you I always start the engine with the electric starter, since the Saabs have a frewheel clutch in the gearbox. On the other hand, my engine usually starts at the first piston stroke. :-)
If I drive my usual path in the night, spring or fall when the halogen headlights needs to be on. I still manage my trips, but the headlights gets so dim after about half an hour that I have to keep the engine running in longer cycles now and then only for charging the battery. I have tried 2x10W LED headlights, but they are not very good for safety reasons and are also illegal (and easy for the police to recognise).
My battery is now in poor condition and can't manage a longer start. On the other hand, it wasn't new when I bought the car six or seven years ago and I have been doing this crazy driving really harcore for two or three years. Weighing in the savings on fuel economy I can easily afford a battery replacement a bit more often than what's usually needed.
Oh, winter time... Well, that's a completely different story! Whe usually have temperatures below freezing point in the winters where I live so a lot of lights and cabin heating is needed. It doesn't take many seconds for the heater to get cold after turning off the engine. Installing an electric circulation pump could help here, but means another amp from the poor battery. The fan also needs to run, at least when I drive slow. Finally I have a huge dog and often at least one passenger, resulting in a need for running the rear window demist now and then.
I've been thinking about adding a super capacitor buffer that could hold the charge for at least a few minutes and allow one start, but their voltage drop and raise so I guess some charging circuit is needed, probably a complicated switch-mode power supply/regulator. An easier way for a normal DIY:er is probably to add a second alternator hooked up with a driveshaft or wheel that to keep charging the battery while coasting with the engine off. That would of course bleed off some energy from the coasting vehicle, but it should be about the same little amount of energy that the engine's alternator have to put back quickly every time the engine is running. Adding the lead-acid battery's initial resistance to accepting the charge, I guess the extra alternator can be a tiny benefit.
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