Yes. First of all a juvenile conviction would not prevent you from owning a firearm (there are a few non-relevant exception) Second of all, only a criminal conviction would affect your gun rights, and your case was dropped. You're good to go for a background check.
Just submit a Personal Firearms Eligibility Check (PFEC) with the California DOJ along with $20 and they will tell your status for sure. But based on what you said you should be ok.
Michel & Associates, PC
All my comments here are intended for general legal purposes. None of my comments here establish an attorney-client relationship with anyone. None of my comments should be relied on in taking legal action without first consulting an attorney.