Yes, in exactly the same way that you can plug a 2400 watt heater or a 5 watt phone charger into a regular household 10A powerpoint, the device (or "load") will only draw the current it needs.
But if it needs more current than any part of the circuit can supply (any part = supply cabling, circuit breaker/fuse, power point, plug, power lead to device), then you are going to either trip the circuit breaker or blow the fuse, or cause overheating to wires or plugs that can lead to fires.
A 20A circuit will be sufficient to allow a total of 20 Amps of current for all devices connected to it to flow through it safely, it will not "pump" 20 Amps into anything that can't handle it. In fact you could still plug in a 40watt light globe into it if you wanted to.
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