The doMobSpawning rule is supposed to not affect spawners, so I would expect that would include trial spawners as well. But it does: Trial spawners will not activate if doMobSpawning is false, and so it does prevent these kinds of mob spawners from working.

To reproduce

/gamerule doMobSpawning false 

Now use /locate to find a trial spawner in the world (this ensures that the trial spawner is properly configured.) Notice that it will not activate (as can be seen by the unchanging color of the block) nor spawn mobs, even if you are in survival.

Then

/gamerule doMobSpawning true

Suddenly spawning will happen.