Do drugs like viagra (sildenafil) counteract the sexual side effects of suboxone?

Yes. All opiates have, as a side-effect, sexual dysfunction. If the problem involves maintaining an erection, medications like viagra, Cialis and Levitra (vardenafil) can help. Others complain that they have problems achieving orgasm with opiates, viagra will not help this. Opiate use, especially long term can result in problems with one's testosterone level. There is a blood test and treatment for low testosterone.
Sometimes. I have patients on Suboxone who have taken viagra (sildenafil) and reported increased libido and better erectile function. Response to viagra (sildenafil) unfortunately is unpredictable and the likelihood of not working is common.