There are two issues raised here.
1. Can an employee take leave during Notice Period.
Legally an employee can take the balance leave in his credit.Many Companies sanction a few days of leave . It is just like availing leave durin normal days.
2. Relieving before the notice period
With due respect to youngsters, I have come across with this as problem with younger age groups throughout my career.Departmental Heads with less experience insist on this. Similarly, youngsters, while negotiating with the new employer, agree to join early.When we select a person. we know he needs to serve the notice period. Instead we ask them to join immediately.We also promise that we will pay the notice pay. But when it comes to relieving, we will insist that he needs to complete the notice period! What a paradox!!!
In my opinion, if an employee wants to quit today, I will relieve him then and there provided he hands over properly and pays the Notice Pay.
Siva