The bullseye will add the risk of the sheet re-cleating as it pulls through, or while you are trying to hold it in your hand for quick gust response.
A more important downside, from my point of view is that once you have the sheet "captive" at that central spot, you can only operate it from the far side of the boat. My cleats are open for that reason: I can grab the sheet anywhere, pull it tight, trim it, and then drop it, from above, in the cleat. When single-handing, I do tie the ends together so I just grab any part of the sheet. (I "single-hand" quite often while not alone in the boat, but perhaps with inexperienced crew - I find it essential to be able to operate the jib sheet from nearly anywhere in the boat, as long as I can reach it at all).
Usually, when I have trimmed the sheet to where I want it, and am ready to cleat it, I'm not in a hurry. If I'm sitting on the high side (so high that I can't drop the sheet by lowering the angle of pull) I do indeed use a foot to help out, but, unlike the need to release the sheet in response to a gust, this operation doesn't have to be instantaneous.
So, I'm happy to optimize for the case where I want the sheet to come off and stay off the cleat, immediately and definitely.
For the depth of the CB top, just drill a pilot hole all the way through, and the you'll know.