In general, yes, although I do have one major exception: paying teachers more would reduce turnover (which is expensive to deal with) and I think there's still plenty of room for improvement in support services: tutors, particularly for non-native speakers, special needs assistance, counseling / mentoring / etc. In many cases simply having a second person in the classroom who could help a kid who's struggling, deal with discipline issues, etc. without disrupting the overall lesson as much would be a worthwhile investment.

This would cost more, although I'd hope we could compensate by having fewer administrators making hard-to-discern contributions at [generally] much higher pay.

I do not think the statement you quoted implies this. Schools could always use more money -- the money just needs to be better spent. The article mentions that a lot of money went to high-priced consultants, some of whom earned $1,000/day. What a teacher could do with a grand a day...

Moreover, the two ideas are not mutually exclusive: the outside-the-home situation could need improvement AND schools could benefit from more money.

One thing article clearly illustrates is that only throwing money at a problem does not work and difficult discussions must be had to improve the schools in this area. This benefits the economy in the long run.

I would say the amount of funding the US education system as a whole currently has is adequate to achieve much better average results than are currently being produced. That does not mean that there are no individual schools/districts which need more money to efficiently achieve better results than they are now. It also does not mean that removing money from the system will not further reduce its efficacy.

You can't fix US education by pouring more money into it, but you're also not going to fix it by dismantling it. The source of the primary problem isn't the education system, it's poverty.

What about the route of lengthening school hours, which would keep kids away from the problems "outside of the classroom".

This would certainly require more money to be put into the school systems.