Could a gum abscess heal with just antibiotics?

Yes, but...: Antibiotics are fully capable of eliminating the visible or palpable manifestations of a dental abscess but those symptoms will recur when you have completed the medicine's course. We use them to control symptoms while we address the underlying cause of the abscess. You will need definitive treatment to prevent recurrence of the abscess.

Tooth related absces: The answer is no. The underlying cause of a "gum abscess" is "dead" tissue which like a "dead" appendix, must be removed. In some abscesses of a single tooth, the "dead" tissue is inside the tooth and a "root canal" removes then may "cure" it. But "gum abscesses" can be a sign of other far more serious underlying causes like jaw cysts or tumors, which can be destructive. See your oral surgeon.