I don't believe scorestreaks count towards the pick 10. I searched around and couldn't find any mention of them in the pick 10. All sites had scorestreaks separate. Plus screenshots show that the scorestreaks menu doesn't have the pick 10 counter on it.
I went ahead and made this class for my pick 10 and I still get equipment and rewards. (If someone can show proof that scorestreaks are part of pick 10, then fine I couldn't find it myself.)
Meh I'd rather a red dot than stalker depending on the iron sights, and I'd rather Lightweight than Ghost simply because I'm pretty confident I can outgun all of the preschoolers and I like the extra mobility. Laser sight looks tempting, might have to fit that in there somewhere.
Sounds OP on paper but if you think about it, running SoH+Quickdraw+Stalker means you lack "traditional" attachments like Ext Mags, Silencer, Red Dot which is important. Kinda like having a naked gun in previous CoDs. You'll also have to sacrifice a secondary or lethal/tactical. But yeah it'll definitely be popular.