No. Not even slightly. Robert Holmes, who wrote "The Two Doctors" stated in an interview:
When I wrote ‘"The Two Doctors"’, it was no mistake that the Troughton Doctor knew he was being controlled by the Time Lords. The theory which myself and other who worked on ‘Doctor Who’ began to conceive was that the Time Lords were in dual control of the TARDIS all the time. The first trial was a mockery, a public relations exercise, because the Doctor had become involved too close to home and something had to be done about him. That’s why he is almost half-hearted about attempting to escape, which normally he never was. He knew that they were in complete control and had been all along. To operate as sneakily as this, you would have to be corrupt, and that’s what came later, when I was the script editor. Did they not condemn the Doctor to exile for interfering in the affairs of other planets? And yet who had sent him on these missions? They had!
His own Target novelisation of "The Two Doctors" contains the following:
Jamie struggled to remember. They had been in a strange kind of garden where the grass was purple and there were flowers as tall as small trees. And although sunlight streamed into the garden, somehow there had been a dense wall of mist all around it. Then three men, tall, wearing yellow cloaks with high collars, appeared out of the mist. The Doctor had bowed deferentially so they had obviously been chieftains. After that... Nothing. Jamie guessed they had placed some kind of magic spell on him because the next thing he could recall was returning to the TARDIS with the Doctor as cheerful as he had ever known him. ‘If I make a success of this mission, my boy,’ he said, ‘it could mark the turning point in my relations with the High Council.’ Then he had found the teleport control and exploded with rage. ‘Of all the infernal, meddling cheek! Don’t they trust me?’ he fumed. ‘Do the benighted idiots think I’m incapable of flying a TARDIS solo?’ He had ranted on in this fashion for several minutes and, since then, had spent his time sulking and trying to detach the offending device. It gave the Time Lords, he explained, dual-control over the TARDIS. Privately – although he was careful to say nothing – Jamie thought that dual-control might not be such a bad thing. On his own the Doctor never seemed able to get the craft to where he said they were going. A snort of frustration, rather louder than usual, came now from the direction of the control console. Jamie glanced round to see the Doctor shaking his head. ‘Unbelievable!’ he said. ‘Do you know what they’ve done, Jamie? They’ve set up a twin symbiotic link to the central diaphragm!’ ‘A symbiotic link, eh?’ said Jamie. ‘Aye, well, I guessed it would be something like that.’ The Doctor shot him a suspicious look but Jamie’s expression was all innocence. ‘Anyway, it would take days to unravel,’ he said, ‘and I can’t spare the time.’ He turned back to the console and adjusted the controls.
This was Holmes' explanation. As he was the person who actually wrote "The Two Doctors", it is the one people should accept as the explanation for what happens in "The Two Doctors". "Season 6B" is a fan fiction explanation that was first created over a decade after "The Two Doctors" aired, and is based on misunderstandings and fallacies.