If by “stack” you mean the height of the front end relative to the bottom bracket, then yes it will go down a bit, and also your bottom bracket will go down a bit.
Relative to the ground the front end will drop (ignoring a few teeny bits) by
[ac] x (degrees slackening) x Pi/180 x cosine(head angle)
where [ac] is the axle to crown of your fork.
Your BB will drop by a around half that, so your stack will drop by around half that.
Plugging some numbers in taken from a random bike on the internet (medium sized Trek Fuel) we have stack 58, reach 44, chainstay 44 (give or take a few mm) fork a-c 50 (in cm). We get around 3mm of drop in the front end. You would need to increase the a-c of your fork by a bit more than that to get the heights back to where they were.