No, he'll write the checks regardless. A big one up front, and then more big ones every month, at least until the children turn 18 or graduate from college. It is what it is. Unless he can prove that she is an "unfit mother", she will almost certainly get custody, so there's the child support checks...
Then comes alimony, which has changed a lot over the past few years, so it depends on (a) what state you live in, and (b) how good your attorney is. She would have a good one.
Then again, maybe the marriage can be saved. I don't know any more than what the media has put out there, so maybe this is a one-time thing...although Lucas' own words at the scene tend to dismiss that possibility. This has likely been a long time in the making, and much like any other smoking pile, all you have to do is add gas (booze) to get an explosion.
So if that's the case, write the checks. In the long run, you'll have a much better life. And career.
I hope it works out for the best, for both of them, and especially for the innocent kids caught in the middle.