Not really. Someone could simply choose to not pay for the standing army and still reap the benefits of being protected. People would be incentivized to do this, and we, as bitcoiners, know that people follow incentives.

Also, the army has to exist before it is necessary.

The sane is happening right now. People who don't pay taxes benefit from being protected. The incentive is clear, to live in peace. Paying taxes do not guarante that.