There was a guy in my CFI class at American Flyers (ADS) that started training 2 months prior to that. By "started training" I mean the fist time he grabbed a yoke was 2 months before completing his commercial certificate.
Granted, he flew for nearly 8 hours a day, probably studied the rest of the waking hours, and did this 6 or 7 days a week. I don't know how much he spent, but I don't bet that it was terribly cheap.
So basically he went from 0 time to CFI/II in about 3 1/2 months. So yes, it's possible. How practical it is, however, is certainly up for debate.
In all reality you will spend less money by doing it all in one fell swoop like this, as recency of experience is prime in this situation, but you will have to pay for it basically all at once, financially, mentally, and socially.
If you're going for a career in aviation, don't sweat which school will look best on a resume. A license is a license is a license. There's too many other variables involved to say that School A makes better pilots than school B, the biggest variable being the student. You'll get out of your training what you put into it, no matter where you go.
Best of luck to you!