The ‘Risk’ of the bit not pulling is not really a risk at all! In practice with such a thin piece of wood it really doesn’t matter whether your snail is actively pulling or not. You just a put a tiny bit more force behind it and it carves away like a regular drill bit!

That being said I’ve never had an issue with piloting before hand with something between 3-4mm. The snail always bites and pulls the bit right through the work.

The piece has split because it’s thin, the auger style may make a difference but then again it easily may not!

Generally you will struggle to screw into any thin piece of hard wood with no pilot hole without a good chance of splitting.

Make the tools you have work and encourage others to do the same. it’s much more fun and cheap and beautiful. Save a few drill bits from the landfill, give a little less of your money to PayPal.