The passing game will definitely be taken away, just by virtue of how elite this secondary is. Last week the secondary was not at full strength and JoeJuan Williams was constantly picked on. That won't be the case this week. The Cowboys will have to go up against the unit that shut down the GOAT a couple of weeks ago.
Now the question remains is how will New England handle that running attack. Too much is made of the average total rushing yards per game that NE is allowing. The fact of the matter is that NE is only allowing 3.8 yards per carry, which is 6th in the league. Teams are averaging 111 rushing yards per game on the defense only because they are running a ton, and they are running a ton because they find it more preferable than passing on this secondary. However, that's not resulting in many points scored for them.
What will end up doing Dallas in is the sheer versatility of this defense, along with Belichick's brilliant defensive mind. We have guys in the front 7 who can line up at any position, and we have guys in the secondary who can line up anywhere at DB. You're going to get a lot of disguised coverages, a lot of creative stunts and twists, and the occasional exotic blitz. I would also throw out that stat about NE playing more man coverage than any other defense. The Pats are a gameplan team, and this week will call for a lot of zone - Cover 2 and Cover 3 with pattern matching and a robber dropping down to take away the short/intermediate routes. Belichick managed to throw off the GOAT with pre-snap disguises. He will have no problem doing it to Dak.
What you should be more worried about is your defense, and the fact that we seem to have figured out the optimal OL combination. If Mac is protected, he will shred that porous secondary.