Left to itself, the jungle would eventually reestablish itself, but the resulting terrain is likely quite different from the original.
Some ecosystems never recover, such as near-desert grasslands that are overgrazed and grow up in cactus and scrub. However, rainforest is pretty resilient, if things are left alone after the original clearance.
Just speculating here but fire and overgrazing strike me as similar in effect. Might an arid grassland tend to remain an arid grassland with adequate rain?