Yes, in the center of Earth gravity cancels itself out. Even if there’s a huge hole making it asymmetric.
With the parachute open, you’ll fall slower and slower until you barely go past the center and then continue to slow down while you oscillate around it. At 32 km/h, you would need about 3 months to get there, but with all the slowing down you’ll probably stay on the path for a few years.






Edit: Yes, my comment was wrong.