Can a student of mechanical engineering with specialization in energy engineering sit for companies where mechanical engineering students sit for at VIT Vellore?

You are eligible to sit in placements. But the issue arises when your profile doesn’t matches with the company. As a B.Tech graduate there is nothing to do with specializations, even though it helps sometimes. Thermal related companies prefer energy. You can also focus on alternate fuels, electric vehicle. This perfectly fits your bill in all Automotive OEM’s