They do indeed. The higher the rarity of an item you donate, the more points you earn (with a few exceptions). Here is the break down:
- r1-r79: 3 points
- r80-r89: 5 points
- r90-r97: 8 points
- r98-r100: 6 points (Sticky Snowball: 1 point)
- r101: 1 point
- r102-r179: 10 points
- r200: Not available to be donated