Legal Question in Criminal Law in California

Of course. You asked 'can he'. He already did, didn't he?

But what does it matter to you since you have now taken your case 'off calendar' by failing to appear, and thus having an arrest warrant issued for you on new criminal charges?

If and when you return to court, voluntarily or in custody, on the warrant, you can again request appointment of a Public Defender, if you qualify.