What are the positive effects of wrongful antibiotic use on a viral infection?
There are indeed antibiotics which have immunomodulatory side-effects, these are mostly from the class of macrolide antibiotics (erythromycin, clarithromycin, roxithromycin, azithromycin) and to some degree from the tetracyclines. Beta-lactam antibiotics (as Penicillin or Ampicillin) have not been shown to be immunomodulatory, but they are among the most commonly used. See reference 1 for more details.

The biggest effect has been shown on pulmonary diseases such as cystic fibrosis or diffuse panbrochiolitis (see reference 2).

Although the exact mechanism of action is not known, Macrolides are know to downregulate the inflammatory cascade and that the reduce the strong cytokine expression of some viral infections. However, these regulatory effects are relatively weak if you compare them to the anti-inflammatory properties of corticosteroids. So the question here is if the advantages are really sufficient compared to the problems, which an unnecessary use of antibiotics may cause. See reference 3 and the references in the paper for more details here.

Antibiotics may be useful to fight bacterial secondary or superinfections which accompany a virus infection.

References:


Immunomodulatory Properties of Antibiotics
Macrolide activities beyond their antimicrobial effects: macrolides
in diffuse panbronchiolitis and cystic fibrosis
Macrolide Therapy in Respiratory Viral Infections