Yes and no.
Higher timing doesn't directly affect the fuel injectors at all so it's not really a way to save fuel, unless you're talking about how the O2 sensor reacts and adjust fueling trim on closed loop. What it does is increase power, IF the original timing is a bit low, and that's how some people feel it improves FC, as they don't step on the throttle as much.
If you increase more than necessary but not too extremely, you only run the risk of some knocking, but the damage is not apparent until you open up the engine and see pitting around the piston face edges.
I assume you mean increasing ignition is done on a distributor-type engine, since coil on plugs don't have the static timing adjustment, which for some is adjustable, but within the ECU itself, but the ECU is usually right, and it's usually the sensor detecting the engine rotation that's the problem.
One of the problems with saying higher timing improves FC is because it heavily depends on cars. A lot of people don't know that for most EFI cars, the ignition is affected by temperature compensation (either coolant temp or Intake temp depending on systems used), especially distributor equipped ones, and the static timing is usually set lower than it's supposed to be due to it being done with the temperature compensation in effect.
For most ECUs there is a procedure ranging from shorting diagnostic plug (honda OBD1) and for some, using a manufacturer specific devices to bypass ignition temperature compensation to get the ignition right with the timing light, for some older cars, usually the manufacturer just specifies a range like 20-24 so if it's within that range, it's good enough. (this is not for all cars, so don't assume 24 deg advance will work on yours without problems.)
Since the power may be better/worse after increasing ignition, on the road, the fuel consumption may be better or worse, as you're basing it on a different aspect. Did you maintain the same throttle? did you drive on the same road? Was the additional power making you go lighter on the throttle/or the lesser power making you step more on the throttle? The actual fuel consumption of cars is based on how it traverses/moves in the internal ECU mapping, so that's why slow acceleration is the main factor in fuel consumption, and if you get the power tuned right, the driver will drive it better, without pressing much so much on the throttle, and there you have your improved FC.
From what I've tested, with closed loop disabled, as do note that this the aspect of measuring FC is different, since when moving, the ECU is not reading the same column and row for fuelling, it is depending on load and throttle opening, and on close loop, fuel adjustments are constantly made. So doing it with the car static, on idling.
Usually FC is better if you tuned for lower power, which means lower ignition values and lower fuel. This is what manufacturers do to keep FC down when car is not moving. This is also why they use 10-16 degrees for static timing for most cars, (with bigger engines using higher since they need the extra power to move the heavier crank and bigger pistons even for idling, maybe overly simplified, but I think this is the simplest I can make it.)
The lower ignition means it needs lower fuel, so it's just enough so that there is no lag when you press the throttle to move. Reducing it more may allow you to run less fuelling in, but not give the best response when you press the throtttle, so people usually tend to press more on the throttle, thus increasing FC, as the ECU will read a different part of the ECU map, thus in the end, the point of reducing ignition and injector duration is not useful to reduce FC.
As to what actually happens when advance or retard ignition.
All this are done without playing with the fuel tables and at idle since I was doing it to show the effects of ignition timing to a friend.
If I retard the ignition on open loop, the AFR will show it being rich, since when you reduce timing from the best point, the engine power will be lower, thus it will read from a heavier load portion of the map, which is richer. This is assuming that I've gone lesser than the optimum ignition point. I would then choose to reduce the fuelling on the higher load part it's in now, but what happens is that I'm decreasing power, but I'm also using less fuel at this particular point in the ECU map. Fuel saving, yes... efficient? not so much.
If I'm already lower than optimum and I increase timing, it will read the lighter load portion of the map because of more power, which is leaner, but the driver will feel the power and thus go easier on the throttle, so higher timing CAN reduce FC, but only if it's below the optimum. increasing more usually makes no difference, just increase the likelihood of knocking/pinging.
On closed loop, what will happen is that the O2 sensor will tell the ECU that it's running rich, when you retard timing and ECU will reduce the injector fueling by a certain amount based on manufacturer's limit for fuel trim. So the effects are not easily seen with a wideband, in fact you might not notice fueling changes at all (unless you look at the higher resolution in m/sec range of the AFR graph...
But on a some modern cars, with a diagnostic computer, can see the amount of fuel trim the ECU does, so it's a reasonable gauge for checking wear and tear items, or parts that are clogged/dirty. If a standard car shows high amounts of fuel trim, then obviously something is wrong/wearing out/dirty/etc.
So if you get the ignition right, it will use fuel to get power efficiently, and that's the best way to improve FC, and that the right foot controls the FC is very true indeed. And that is also why the some of the best tuning methods involves control of the ignition timing of all high and low load points, across the entire RPM range.
Higher igniton doesn't mean better, but it is better if your original ignition is a bit low.
As far as I know, if the timing is advanced, engine power will increase as well until some point, after that knocking (or pinging) will occur. Anybody has done it before?
