At the risk of advocating unnecessary perfectionism, I see that centre plate as performing at least 3 functions:
1. increased structural integrity of the dish, particularly the centre area
2. if there are viewing holes in the dead centre of the disks (one on the front, one on the back), then visually checking for symmetry of the dish with strings is easier and more accurate
3. anything which seals out insects from building nests inside the ends of the tubes supporting the mesh is good.
But as noted above by those more experienced than I am it is not likely to affect your signal except marginally.