Actually long before the planet was in danger of touching it's star, it would become a star itself. Consider the diamater of the Sun: 864,000 miles, vs. Earth's distance from the Sun: 92,960,000 miles. So as you can see before the planet got even 1/92nd of the distance from the star it was orbiting around it would go critical.
I'm questioning whether the mass increase of the planet might actually send it out of orbit, or into the star before it reached critical mass so drowning the star may have actually been a relevant question.
