How structural (if at all) is this piece in the rear?
 

http://986forum.com/forums/uploads02...1505537633.jpg

It's literally called the "rear support" in the parts diagram. It attaches to the body up top and the rear of the bottom plate at the bottom. It's handy to jack from. Is it tying the body together in any sort of way that would compromise handling if removed? Or is it simply to reinforce the bottom plate and help protect the back of the transaxle?

Yes all of the above, jacking point is under the other side of the aluminum plate where the steel brace is

Yes and no.

Yes, its there for a reason and probably adds some rigidity to the suspension and protection but its not going to create a dangerous situation if the support or the plate is removed.

Last year at AutoClub Speedway I went off track and bent the rear plate. Back in the paddock, we removed it in a few mins and I raced the rest of the weekend without it. There was no change in handling even at 135mph on the NASCAR banking. I did replace it before the next race mostly because removing it may not be a legal modification in Boxster Spec.

There is a discussion of this plate in the middle of this thread:
http://986forum.com/forums/performance-technical-chat/63248-shoutout-technobrace-pedro.html

I removed that brace for awhile as I was testing a muffler I built. I drove my boxster around without that brace for a few months and even tracked it twice. Didn't notice any difference and only put it back on because I figured it had to help and didn't weigh that much.

I had to remove it to fit a new exhaust. It might have it modified to be shorter and not tie into to the plate. But, doesn't seem like it will affect things too much being out.