Is an automatic transmission dust cover needed?

I'm in the final stages of getting my car all ready to start and I came to the issue of what to do with the transmission dust shield. The car is a 73 dart, 360/904. I left it out currently so I could more easily put the converter bolts in but now I'm wondering If I have to put it in at all. Would it give more airflow and because of that cool better? Or will I get lots of crap in there? I can get it into place easily anyways, just wondering if its really needed.

And what is that little brace thing in the picture, it came off of the 318. Is it needed? because I cant get it onto place with my headers.