If you’re only going to put a couple pounds in the pockets to serve as trim weights...I don’t see a problem. That being said...that pad is going to be fairly positively buoyant, so you’re likely going to have to add 4+ lbs just to offset the pad.
That’s not getting into the thought that adding 12lbs (maxing out all four pockets) to somewhere you can’t readily access during a dive (if necessary) isn’t a good idea. Why not just get a regular/metal BP?
That’s the main reason that I removed all of the padding from my HOG BP setup. Anything padded (ex. BP, shoulder pads, etc.) is positively buoyant and requires weight to sink it. Even my 10lb HOG pouches were positive.
Most of my dives are shore dives with a ~100’ walk to get to the water. The “comfort” issue with a metal BP that people use to justify a soft plate is a non-issue. All using a soft BP does for you is make it necessary to carry more lead.