It does, but it gets progressivelly harder as it goes up to maintain enough vertical airflow for a rotary-wing craft to stay up because the air becomes thinner.
The going faster for fixed wing craft compensates for the air being thinner because the Bernouli Effect (the sustentation effect from the wings) gets stronger the faster the airflow over the wings is, but the equivalent of that for a rotary wing craft is for the paddles themselves to rotate faster and the craft itself going faster doesn’t help (it makes air over some paddles go faster but also makes the air over the paddles going in the opposite direction go slower).
Quadcopters are rotary-wing craft, so can’t really improve the altitude they can reach by going faster.