Its most likely a very trivial question but central heating systems aren't something i'm familiar with, I've had a good dig around on the internet and cannot find any reference that states that specifically using central heating consumes water, not considering any other form of water consumption e.g. using the shower.
Only if you have a humidifier installed, and in that case it would be a very small quantity.
To determine whether your system has a humidifier, examine the primary ducts near the furnace unit. Look for a tray or housing with a water line and possibly a power cord.
Here's an example. Notice the unit attached to the intake duct. It has a copper supply line and a PVC drain line.
Central heating should not significantly increase your water usage. Though depending on what type of central heating you're talking about, it may consume some water.
Typically forced air heating will not consume any water. However, if it's a gas/oil forced air system, a humidifier may be required. The humidifier will consume water, though not a significant amount.
Obviously if you're using water to transfer heat around the home, you'll have to fill the system up. You also might have to add a bit here and there during regular maintenance.
If there's a leak in the system, and the system is automatically refilled. Then water could be consumed, but how much would depend on the severity of the leak.
Electric heating will consume no water, unless you're generating your own hydroelectric power.
Geothermal should not consume water, but may require water if the energy source is a lake/pond.
Burning solid fuels should not consume water, unless humidification is required.
You may have disqualified this already, but I thought I would mention it.
We humans are complex creatures. We (and our pets) may consume more water when the heater is running. I Will give you an example.
Here in Florida, we (my household) consume 25 Gallons of drinking water a month during the summer. During the mild parts of the spring and fall we consume around 7 gallons. During the winter we consume around 20 gallons.
The reason for this is simple. In the summer it's hot. In the spring and fall it's very nice. During the winter however it's quite cool, and keeping the house warm means running the heater. When the heater is running it pulls a lot of moisture from the air. The humidity in the house drops and we need to drink more water to replace what we loose.
It may not seem like much but it makes a big difference in the amount of water we consume. Keep in mind that the humidity here in Florida is normally quite high, and we are used to it.
The heater it's self does not consume water, but the people living in the house alter, slightly, their consumption.
These numbers were gathered with some tracking to find out how much potable water would be needed on a house boat long term. They are accurate for this house, but the point of the tracking was not to have any limits and simply track what was normally drunk.
If your system is an open loop geothermal heat pump then your water usage would increase dramatically with the heat running. These systems draw heat from ground water and then dump it down a drain.
With all other water turned off, when your heat turns on, do you hear water running in your utility room?
These systems are becoming more popular in rural areas with well water but they are not used with municipal water systems because of the cost of the water.