The court won't make the decision about timings. It'll be decided effectively as an administrative exercise.
As an example (made up! I know nothing!) the GMC - who are basically the prosecution - will say, "We have four witnesses. Here are their statements. The first witness will take this long, the second that long..."
The defence will say, "We've read their statments. We need half a day to question the first witness, and an hour for the second..." and so on. And then they'll say, "We need this long for our witnesses."
Plus they will estimate how long they need for their opening speeches, and their closing speeches.
Then an administrator will say, "Usually in cases of this complexity it takes two days for the panel to make their decision and write it up."
Then all that will be added up, with a fudge factor, and that'll be how long it'll be listed for. The tribunal panel will have no say in it.
In terms of the broader political context, I wouldn't expect the GMC to raise any of that, because it's not relevant to the charges that the panel are being asked to consider.
The defence might raise some of it, if it thinks the context will make the panel consider the tweets more likely.
But, no, I wouldn't expect anything about experimental treatments, or other cases to feature. The charges are actually quite limited ('You posted these things, it was nasty, some of it was threatening') and I'd expect both sides to focus quite closely on that. If anyone is expecting this to impact on the wider issue of care pathways for people who identify as trans then they're going to be disappointed.