The phrase "so engaged that" is correct and usable in written English.
It is used to indicate that someone is so deeply involved in something that they cannot be distracted from it. For example, "He was so engaged that he didn't even notice when the fire alarm went off."
Disputing charges that the Obama administration is shedding commitments, Kerry said that "you cannot find another country that is so engaged, that is partnering with so many Middle Eastern countries on so many fronts".
It's even better when they are so engaged that they call him.
In the technical area he was so engaged that he once juggled and another time shimmied.
What puts you in a flow state, where you're so engaged that you don't look up from your work for hours, and suddenly it's 5 pm?
But he is always businesslike and polite, and so engaged that you would never sense that this is probably the umpteenth time he has discussed his new film.
In other words, teachers want their kids to find "flow," that feeling of complete immersion in an activity, where we're so engaged that our worries, sense of time, and self-consciousness seem to disappear.
"Melissa is so engaged in that conversation.
Doing that, he brings himself within the requirements of the statute, and it is enough to charge that he as so engaged, and that while so engaged he did demand, receive, and retain more than the sum which by the statute he was permitted to do.
Goodman seems so jaded, so hostile, so barely engaged that speaking to him has become a little unnerving.
"Media and film are popular because of the skills students develop, and the reason they're so engaged is that they're learning about things affecting them now".
The two men had the prescience to negotiate a 50-50 split on all digital revenue with Comedy Central, and part of the reason they remain so engaged is that they have real participation in the "South Park" enterprise.
