Squeezed,
As you'll know, it's not the MiDYiS tests that actually set the benchmark for your child's targets for secondary - it will be their SATs results, because that's the way that the system works at present and the school can't over-rule that.
I think it does also depend a lot on the school how much SATs impact on the whole of Y6, and how much focus is put on that single week.
In some schools, there is no point whatever in withdrawing them from the SATs themselves, as it is the endless preparation and coaching towards them that narrows the curriculum for the children all year that is the real problem. It's a case of withdrawing them from Y6, or nothing - the tests are the lowest key part of the year.
In other schools, the tests are so low key that they are barely noticeable (my DC's primary managed this quite difficult trick - they had a week every year in which children did tests, and the Y6 one looked so exactly like the previous years, and had no extra explicit preparation for it, that the children didn't really notice them). In this case, there would be a political point in boycotting the tests as part of a wider, political boycott (i for one would support such a boycott, simply because so many schools are becoming 'all of Y6 is about SATs) but not to spare the impact on your child, because that would be minimal.
There are some schools where the preparation for SATs is very low key for much of the year - usually the first two terms - and then ramps up very, very significantly after Easter. These are the schools where a boycott would be of benefit to the child - though such a boycott would have to be quite long, and have to involve the preparation as well, because it is that 'build up' that is worst for the children.
As i say, I would support a boycott, especially if this was planned from long enough in advance to give ALL children a totally SATs-free Y6 - ie it was clear from September that SATs would not be taken. I know that in the last SATs boycott it was only the test period itself that was boycotted - by which time most of the damage in terms of stress and curriculum constraint had already occurred and could not be undone.