This is a boostrap winding, which as you require, will supply the IC's operating current.
Before the unit starts operating though. you still require a startup circuit, which takes the high voltage rectified DC and drops it to the lower voltage required to start the IC.
The simplest implementation is a power resistor, a capacitor and a zener, as simple as that.
Having said this, when you do your calculations, you will realize that dropping from 310 to 10 volts DC with a startup current of 30 or more mA like the 3525, the resistor and zener will be very, very large.
This is because the SG3525 wasn't designed for transformerless line startup. Newer devices have startup currents of perhaps 1 mA or lower, allowing for much smaller components.