Yes, but at the expense of having to always draw 1A from the mains, irrespective if it is on or off. It is best for a draw of under about 20mA, as then you do not really have to worry about power draw in the on or off condition, as they will be small. As well remember that this entire circuit is at mains potential, and all parts and anything connected to it that is not isolated by either an optocoupler, high voltage mains rated capacitor or at least 2mm of plastic in 2 separate layers ( basic Class II insulation requirement) will be at either mains or some other potential that is close to it, and with the capability to deliver a fatal shock.
Drawing 1A means you would find a transformer, rectifier, smoothing capacitor or a proper isolated switching power supply will be smaller and lower cost. To draw 1A means the capacitor has to be a value close to 22Uf 400VAC rated, a capacitor that big is at least the same size as a can of cool drink, and about 5 times the weight of a full can. Switching so big a capacitor on as well, and discharging it when the power is off as well, is not easy, the switch has to be rated for 20A at least and then you need inrush limiting and a 10W bleeder resistor as well across the capacitor.