Yes it absolutely can cause you issues. Most modern cars have to have the coolant all the way filled and burped (any air in the system removed) or it will not function properly. Given an example of my 2003 Civic. It had a small head gasket leak where it would burn a small amount of coolant every time I drove it. If I did not keep up on the coolant (refilled it every time I drove the car), it would overheat. So even low coolant will cause problems.
If you only have one litre of coolant in a system which requires 7 liters to be full, you have an issue where the coolant level most likely doesn't even reach the level of the coolant pump, and therefore will not make the circuit through the engine to start too cool it. You will most likely start to overheat very quickly and will cause damage not much longer after that.
Even with only 1/2 the coolant in the system, you will most like be exactly the same as only having only a single liter. The coolant may reach the level of the coolant pump, but will only have coolant in spurts. There will be massive hot spots which will form inside the engine, which will again cause overheating and damage if driven on too long.
Any which way, having the proper amount of coolant in the system is the only way to go. Without it, you are committing your engine to a heinous act of self destruction.