If it's a 'Standard' DBS check (such as for people who work in the legal profession, security industry, etc but who don't normally work with children or vulnerable adults) then the answer to your question is definitely 'No'.
If it's an 'Enhanced' check (such as for those who work with children or vulnerable adults) then it's up to senior police officer to decide whether information held by them should be included in a DBS check.
Since the Soham murders (where unproved allegations against Ian Huntley were omitted from his CRB check for employment as a school caretaker) the police have tended to 'err on the side of caution' and include unproven allegations in CRB/DBS checks.
For example, there's been a post on AB from a teacher who found that his DBS check included an allegation that he'd attempted to groom a child for sex. The police had included that allegation despite the fact that neither they nor his employer had ever spoken to him about it and he was totally unaware of it.
So unless the allegation against you was dropped because it was definitely shown to be false (rather than just through insufficient evidence to secure a conviction) there's a possibility that it will show up on an 'Enhanced' DBS check. That possibility will clearly be higher if the allegation is directly related to your type of employment (such as assault on a child if you're a teacher) than if it's got little or nothing to do with it.