"How much noise is too much and what is your basis for comparison"
Here's an MP3 I recorded of the noise it makes while draining ( I had to zip for the upload to work). It's a violent enough sound that I can feel it in the tub and surrounding walls. It's loud enough to hear it through the walls and on the first floor. For comparison I only have my memory of what other tubs I've used sounded like when draining. The old tub I replaced drained so slow it can't be used for comparison. Also, my sink and lav drains sound "normal" to me. Just that quiet rush of water through the pipes.
The length of the tail piece is 14".
Another thing. I was wrong about the overflow not sucking air. I failed to cover the two holes that are tapped through it for the screws that hold the overflow cover plate. I tried again with the plastic film over the front and my thumbs over the 2 holes in back. With the overflow completely blocked, the gurgling sound goes away and all I hear that familiar sound of water rushing through a pipe. When I uncover the screw holes I can hear air being sucked into them and the quiet rushing sound is replaced by that noisy gurgling again. The tub definitely drains slower but it's about what I would expect. It's able to make a small tornado at about 2". With the overflow sucking air and making noise, the tornado started at about 4" then turned into a hurricane.
I thought the vent was suppose to supply the air to the drain. Is it normal for the overflow to suck air?