Is it possible that post-root canal infection will not recur when antibiotics have cleared it up?

It's possible: But it depends on what caused the infection. Residual bacteria in bone? Leaking restoration? Fractured tooth? Debris in canal? Hard to say what applies in your case.

No: If the antibiotic was caused by a flare-up post root canal, then it should be fine. However, if the infection was caused by bacteria that may still be in the tooth, or a missed canal, the infection can come back. If the tooth is not restored properly with a permanent filling, the infection can come back. If there is a cavity still present, the infection can come back.