Yes — Bellick does get out of Sona.
When Michael Scofield eventually orchestrated the escape from Sona in the episode "Hells or High Water," Bellick was not on the guest list.
Following the "official" escape, the power structure in Sona completely collapsed. In the confusion, T-Bag started a massive riot that resulted in the prison burning down. During the fire and the subsequent breakdown of authority, the remaining inmates—including Bellick, T-Bag, and Sucre—managed to flee the facility.
Spoiler Alert: This post contains spoilers for Orange is the New Black seasons 1-7.
Brad Bellick's journey in Sona was a brutal fall from grace. He began as a feared captain at Fox River and ended up as the "lowest of the low" in the Panamanian hellhole.