Did Luke have a plan when he jumped into the chasm in Empire Strikes Back?

Luke's plan was suicide.

From the new canon "Star Wars: The Empire Strikes Back: So you want to be a Jedi?" novelisation of the film

You want to be with your father. More than anything in the universe, this is what you want. It is what you’ve always wanted.
But Vader is not your father. Not anymore.
You let go of the platform and fall into the abyss.

And the Star Wars in 100 Scenes factbook

Despite his agony, Luke senses the truth of Vader's words. He has another choice - to die. He lets go and falls down the reactor shaft.

This is backed up by the film's junior novelisation

His voice is so hypnotic, Luke thought, and felt part of himself falling under Vader’s spell. But only part of him. Luke looked down into the deep shaft that seemed to stretch down to forever.
“Come with me,” Vader urged. “It is the only way.”
Luke looked directly at Vader and felt a certain calmness as he thought, No. It’s not the only way.

and from the film's official novelisation

His Father...

With the calmness that Ben himself and Yoda, the Jedi Master, had taught him, Luke Skywalker made, perhaps, what might be his final decision of all. “Never,” Luke shouted as he stepped out into the empty abyss beneath him. For all its unperceived depth, Luke might have been falling to another galaxy.

and from the film's original script

Vader puts away his sword and holds his hand out to Luke.

A calm comes over Luke, and he makes a decision. In the next instant he steps off the gantry platform into space. The Dark Lord looks over the platform and sees Luke falling far below. The wind begins to blow at Vader's cape and the torrent finally forces him back, away from the edge. The wind soon fades and the wounded Jedi begins to drop fast, unable to grab onto anything to break his fall.