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Yes. Though 2 PCs will be hard, especially for kids since you'll lack a diversity of ways to solve problems (e.g. skills, tactical options, etc.).
If you're concerned that your kids will have difficulty with certain sections because they lack the necessary resources of a 4 person party, you can always add an NPC or two to the party and adjust the encounters accordingly.
The Bestiary includes a full set of rules for adjusting encounters (up and down) for party size, and how to adjust individual monsters (up and down) to achieve the appropriate difficulty level.
I have a party of 6, so for each encounter I make the adjustments when I prep for the session, noting how much I need to scale up the encounter and then I physically write those adjustments in the Doomsday Dawn book at the encounter so I don't forget.
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The only mention that I've found is in the introduction to Doomsday Dawn, under "Adjusting Encounters":
Pathfinder assumes that the typical group consists of a Game Master and four players, but often a Game Master will find that the number of players interested in her game doesn't always align with this expectation.
Since it's not mentioned, I assume that you're free to have as many or as few as you want. The survey itself leaves "Number of PCs" as an open text field rather than a drop down, so I assume Paizo is giving GMs flexibility here.
I've been running for a party of 5 myself. It's not too hard. These are the adjustments I made for the extra person and an actually well balanced party:
* Half an elite template (+1 everything, +5 hp) for the ooze.
* Added a goblin dog to the first goblin encounter, and had one of the goblins spend a few actions to mount and start riding it into melee while the others focus on range.
* Goblins flee into the fungus room once "knight goblin" is down.
* Change one of the centipedes into a larger full elite (+2 everything, +10 hp) as a "queen" to have something less squishy and more interesting. This maybe should be another half elite though for a less competent group.
* Change the 6 skeletons to 4 skeletons and 3 zombie shamblers for variety and to give the players a chance to see weakness in action before the quasit fight.
* Add homunculus to the quasit fight. For flavor I gave it the water type and replaced its fly speed with a swim speed, tying the poisonous little bugger to the polluted fountain, basically making it a weaker water mephit.
* Added a reskinned kobold scout to the second goblin room as the leader / person who built their deadfall trap.
* Kept Er-rat-ta the giant rat in Drakus's room due to the extra PC.
Since I had previously run the PCs through stuff from Rose Street Revenge as a "session zero" game to get used to their characters and the rules before the actual first Doomsday adventure, I also connected them. The bloody barbers were kidnapping people and trading them to Drakus for drugs to sell (so Drakus actually has a food supply), the trade back and forth was handled by the Sharks as middlemen, and the drugs were spores scraped off the fungus in Lost Star, so I put a workbench with paraphernalia in that room.
Ditto on seven. I played session one of chapter two with 7 then split them into two groups for session two.
It wasn't any worse than pf1 with 7,but 7 is just too many.