The route you should actually take is: Yercaud - Salem - Omalur - Thoppur(left)-Mettur-Male Mahadeshwara hills-kollegal-T.Narsipura-Mysore. AFAIK
until thoppur you can zip fast, post that you don't get to see double roads until mysore, the road conditions are unknown and im sure it won't be good considering the heavy showers of late.
Or it would be better if you can take this route: Yercaud - Salem - Bhavani - Satyamangalam(Ghats) - Chamarajanagar - Najangudu - Mysore
Feel this is the better road because until you climb down Sathyamangalam, the roads though single lane from Salem are very good,but once you enter K'taka it's pretty bad until Nanjangud.
However the ghats are little tough to navigate as this is the major route for trucks.