Can you use a 10 Amp socket (and device with a 10 Amp draw) on a 15 Amp circuit
Yes, you can use a device which draws 10 A on a circuit protected by a larger breaker. For example, table and floor lamps may draw less than 1 A and have light power cords that could not carry 15 A continuous, but code allows them to be used on 15 A circuits.

If the lamp socket would develop a dead short, the breaker would blow before the cord would overheat. If the lamp socket would develop a fault in which it drew 19 A continuously, then the lamp cord would get hot, but the probability of such an event is judged to be nil.