I have made 6 kits so far,
4 were not Filtered, 2 have not yet been tasted (still too young) and 2 have been. The White that I made - VR Liebfraumilch was and still is perfectly clear with no "Chunks"
The red however is really difficult to catch that odd bit of oak chip that missed the racking, and occasionally 1 in 3 bottles I find a little flotsam in my glass.
I got my Mini Jet and used it to filter my other 2 over the weekend.
It came with #2 filters, so I used them to filter the Mezza Luna, and I bought a #1 for the Pinot Noir.
Once the #2's are used - I will get the #1's and use them purely just to get the "crud" that may still be floating after racking.
So to answer your question: Yes Finings can reduce the amount of bits, but I think that you always have the possibilty of bits if you don't filter.
I know that I will probably filter all from now on, but as I say, only using the #1 (coarse) to get rid of the itty bitty oak and seeds that may be missed in racking