Not necessarily...
Firstly, there is ever growing evidence to dispel the myth that organic/non-conventional produce is superior to conventional produce in terms of health & nutrition; organic produce and conventional products have similar nutritional and health benefits.
Secondly, there is no control or regulation over the term "organic" which means that anyone or any company may use this term in their labelling and advertising without any justification. In fact, the labelling & advertising terms on products are intended to manipulate and infer a better/superior status or product (unlike drugs/medication, labelling regulations are very lax and do very little to protect the consumer when products are classed as food, supplements, cosmetics or personal care products)
Thirdly, there are a variety of "certified organic" logos used by differing certification companies; each certification company/body have their own set of "standards". These standards may greatly vary from one body to another.
Fourthly, many people are misled to believe that "organic" produce are free from pesticide/fungicides or additives, due to the misleading advertising/labelling and false claims!
Nothing is further from the truth. All commercial produce utilise agents & additives to ensure their products survive, look, feel and taste their best. Unfortunately, the truth is, organic produce end up using significantly more organic/natural pesticides/agents, simply because the agents used are far less effective than conventional agents.