Stormonu
NeoGrognard
With my kids I have usually just taught them at the table. I also have done similar to what the Beginner Box is going to do as well - we don't use AoOs and limit combat maneuvers.
The oldest who is almost 8 I started playing with at age 6 in this fashion. He has a great attention span though, is mature for his age and is sort of a geek like his Dad. He's been just fine with the game and knows the basics pretty well at this point. I've also had him help me test combat from a few other systems as well and he usually picks that up very quickly.
My youngest I started letting her roll some dice and hang out while we play. She's four. She knows nothing of the rules, but rolls the dice and participates in the story for about the first 60 to 90 minutes.
I think it is worth a shot. Just do as you have already noted, keep the action exciting and I bet it goes well. This Beginners Box should be perfect for you!
Similar experience here: I started playing with my 5-year-old with the 3E boxed set (the one with the Black Dragon mini) and he loved it, caught on pretty quick. He's ten now and sometimes DMs his younger brother through adventures he made. My younger son is now 8 and likewise has been playing since age 5, but is near-autistic. Keeping him on-task in the game for more than 5 minutes can be difficult, but when he's paying attention, he loves to play and can be surprisingly clever.
In both cases, we tend to keep the rules "behind the screen", the kids have fun enough exploring, fighting, rolling dice and hamming it up with NPCs. Dad (and Mom) worry about how the rules work and adjudicating whether an action will work or not (sorta reminds me of the days of 1E & 2E).