You will probably be fine without it. I forgot to put it back in on the CJ5 I used to have and nothing bad ever happened. It does help keep mud and crap out of the bellhousing and clutch though.
Also it will put the tip of the trans input shaft like 1/16" (or however thick that plate is) deeper into the flywheel. Same with the distance between the clutch fingers and the throw out bearing. But it really shouldn't be enough to cause any real issues
I had a buddy who did that too on his Dakota, and he just cut the bottom half off to where he could bolt that part of the cover on to keep crap out of the bellhousing, but didn't have to pull the trans back out to get the whole thing in. He never had any issues either, I still see the truck driving around time to time
