Yes. Although the charge and consequences of a no-injury assault will generally be relatively light, one may be charged even in this situation. Depending on whether the person has any prior criminal record, whether this was a domestic violence situation, etc, the consequences might be increased or decreased.
David C. Beyersdorf
DISCLAIMER- THIS IS NOT INTENDED TO AND DOES NOT CONSTITUTE LEGAL ADVICE AND DOES NOT ESTABLISH AN ATTORNEY-CLIENT RELATIONSHIP. CONSULT QUALIFIED LEGAL COUNSEL IN YOUR CITY OR STATE FOR IMMEDIATE LEGAL ADVICE.
---
It is a common misuse of the word "assualt" in a situation like this. Assault is defined in the California Penal code as "an unlawful attempt, coupled with a present ability, to commit a violent injury on the person of another." (CPC s 240). In other words, shaking your fist in someone's face while saying, "I'm going to knock your block off" is an assault.
What happened here was probably both an assault and a battery. A battery is "any willful and unlawful use of force or violence upon the person of another." (CPC s 242). A battery is when actual unlawful force is used - such as pushing someone down.
Most prosecutors in California will argue in court that any unwanted touching, if done in anger, is an unlawful battery.