Is it dangerous to request more power from a mains circuit than intended?
The main purpose of circuit breakers is to protect wires in the walls from overheating.  Even sprinkler systems cannot access wires in walls to put out the fire; the fire can become fully engaged.  

You are messing up. You should not overload the circuit like that.

Your local government probably has provisioning standards for electrical supply.  For instance in the US, we must provision power for 125% of continuous loads + 100% of loads not continuous.  Many things such as a heater or EVSE are designated continuous loads even if they are not continuous.  

So if I want to put a 1200VA water heater and an 800 VA garbage disposal on a circuit, I must provision 1200x1.25 + 800 = 2300 VA.  That just limbos under the 2400VA capacity of a 120V/20A circuit, so it is alright. 

Stay within the provisioning limits of the circuit.  If you need more, either provision it or move the loads around physically to get them on different circuits.  This is often a blindside of Bitcoin miners who want to put 10,000VA of miner all in one room (never mind the cooling problem that creates!) Spread them around the house so they are all on different circuits! 

Trip curves

Circuit breakers have a designed trip curve.  They will trip when current draw and time match the trip curve, with some tolerance.  



This example (thanks Tester101) shows this breaker will: 


at 2x rated current, trip between 9 and 35 seconds.  
trip in 1 second with an overload between 4.5x and 8x. 


These numbers vary due to manufacturing tolerances.  Note that the Square D does not vouch that it won't trip at 100% load; it only says it'll take at least 300 seconds to trip.  

You should look up the trip curve for your breaker.  Its behavior should match this.