Yes, it did get airborne for a few seconds but from the video below, it looks like the left wing was damaged by the fire and could not provide enough lift, then the right wing rolled the plane to the left causing the crash.
https://bsky.app/profile/shipwreck75.bsky.social/post/3m4tvh...
The wings and aerodynamics don't really care if air or air with combustion are flowing around them.
Roll is a consequence of the loss of control due to low speed and the yaw of the good engines. Speed up, rudder works, plane might maintain positive climb.
Not saying it's what happened here, but if the heat is intense enough to deform the wing / control surfaces, it matters.