I expect that you read my contributions to your previous relay question.
This case is more complicated because of the capacitor. If there was no cap, the answer would be - no problem - provided that the relay current does not exceed the maximum allowable LED current; see the LED spec.
But with the cap (and I assume it is 100 uF not 100 nF) there may be a damped ocsillation and therefore it is possible that the reverse voltage of the LED could be exceeded.
You obviously need the cap to provide sufficient operate current but allow the current to be reduced once the relay is operated. Do you know the operate and hold currents for the relay? (they may be expressed in voltages) Do you know the coil resistance and inductance? If not, can you measure them? Do you know the operate time?
The reason I'm asking these questions is:-
1. Once the relay is operated and the cap has stopped charging, the relay coil current will be determined by the LED voltage and the supply voltage. If you really want to minimise the power dissipation, then you may need a resistor in series with the LED so that the coil current is just enough to hold the relay.
2. You need to know the inductance and resistance of the coil in order to determine whether the circuit is overerdamped, critically damped or under damped. If it is under damped, there will be a damped oscillation when the transistor is switched off. The critical question is - what is the amplitude of that oscillation. If it is too large it will damage the LED and possibly the transistor.
So if you can measure these parameters, you can simulate the circuit using a software package such as Switcher CADII and see what the amplitude of the oscillation is.