First, welcome to the game! There are plenty of coaches willing to help you get up to speed.
Now to your question: You absolutely have a chance getting DII recruits. It's important to remember DII recruits won't sign with DIII teams until the second recruiting session, the one at the end of the season. If you ever go after DIII recruits, those can sign with you in the first recruiting session, the one mid-season.
And there are a lot of variables that contribute to whether a recruit will sign with you. But the short answer to your question is, yes. there's a chance.