Probably not. Your gallbladder produces bile acids that are emptied into you GI tract to help with the digestion and subsequent absorption of fat. Thus individuals who have had their gall bladder removed may experience some problems with the digestion and absorption of foods that have a high fat content.
Acne is a result of hair follicles becoming plugged with oil and dead skin cells. Medical doctors do recognize a relationship between adult acne and poor liver and bowel function. Chinese Medicine sees a relationship between adult acne and both liver and gall bladder function.
Diet can have an effect on acne but the main reasons for triggering or aggravating acne are (1) male hormones, also known as androgens, and (2) some drugs, such as glucocorticoids taken for the long term treatment of inflammatory disorders such as arthritis, or lithium, which is used for some mental disorders.