Self-oscillating converter circuit
Sure, it is a self-oscillating flyback.
If you don't need primary to secondary isolation, stacking the windings gives a little higher output voltage.  
Yes, if the transformer has any significant leakage inductance (it will) then a snubber is a good idea to protect the transistor.


Having said all that, this circuit's operation will vary a lot with component tolerances, and the efficiency and reliability may be poor depending on the switching frequency.

I would recommend using a modern boost controller and MOSFET for a more efficient reliable design.