I would not fill up an application unless verifying with HSWA to make sure that the information is required. I was asked to fill up an application for the 5250 years ago, and the AD sold it to another customer. At the end, the AD knew all of my collection and my info, and I didn't gain a thing.
Based on my experience, you want to make sure that AD's are not using the form to size you up as a customer, as it happened to me. According to my current AD, the pieces are allocated to the AD by the distributor, and the AD will ask for the customer to fill up the form afterwards to inform HSWA who the piece is being sold to. I've never filled up a form until a piece is already allocated and about to be delivered to the AD.
As far as the 5270 is concerned, I have not heard from my AD that it is an application piece. The 5170J certainly is not an application piece, yet I have seen previous postings from customers stating that their AD's asked for the form to be filled. Just for your information.

I have an offer from my AD recently. No application needs.