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I've never bought these new, so I don't know what kind of instructions they come with, but to me, it made sense to put some tension on them. I tightened the end bolts so that there is a bit of pulling tension on the bar. I didn't do any comparing to what it feels like without the tension, but my suspension is really tight. It seems like some tension makes it less likely for the whole trapezoidal unit to flex.
Does anyone have specific insight about this?

The strut bar is a "2 force member" (ideally). That means that it's either in tension or compression all the time. In this case, the outside wheel in your turn is deflecting it's strut tower outwardly away from the center of the corner. The strut bar is designed to let the inside strut tower act as an anchor to limit the deflection of the outer one. Setting up the strut brace in slight tension will basically pull the towers together when at neutral deflection, so the "anchor" starts pulling on the outer tower sooner when you start cornering.

It could actually help. I think the amount of tension you can put on the bar is very small in comparison to cornering forces so really it won't be noticeable at all. But I imagine that someone in a high level racing application has put quite a bit of thought into the question you've asked and designed their chassis accordingly.