Do teaching evaluations improve from high participation rates
There are too many forces here to expect any clear trend. 

It depends on who forces them, I think. You are probably correct that when they are optional, only the most invested will be likely to participate. But if the instructor forces them, then some, taking it as an extra task for which they see no personal benefit, might react badly. I'm assuming anonymous responses, of course. 

If the system, somehow, forces them then those less invested might still be annoyed, but not at the instructor. Whether you get honest answers, however, or chaotic, playful, anarchistic ones or helpful ones would be worth looking in to, but there is probably no real way to do the experiment. 

However, the comments are likely to align, more or less will with how pleased the students were with the course and the instructor's helpfulness than otherwise. But this might not give overall trends different from the current situation you find. 

But in particular, I don't see any forces that suggest "yes-men" behavior. 

But turn it around. If you do a really good job or a really bad job your participation rate will probably go up. 

Humorous aside: Or, you could bribe them somehow to participate so they see a personal benefit for answering. Tricky to do a bribe that doesn't itself slant the results.