You might be shooting yourself in the foot.
This likely depends on high personal productivity of the author, and if you cannot sustain the pace, I think you will lose whatever audience you gather.
It will also depend on your writing style: I could not take this approach at all, I cannot finish Chapter 1 and make it shippable without having written the rest of the book, I go back and change things all the time, to fix up character motivations or traits, or add foreshadowing. Even after finishing a book I go through multiple reads to double-check my story holds together, my characters are consistent, that I have color (literally) in my descriptions, that I haven't written walls of exposition or dialogue, that I eliminate redundancy and pick better words, and so on.
I do finish books, but I have to finish a book before the first page is ready to be seen. The book I just finished has had the first page revised about ten times, and the first three paragraphs probably twenty times, several times after I finished the book.
But, let's say you are confident your first chapter will never need revision in any way. How long would you stick with a story if the chapters come out sporadically? It takes me roughly nine months to finish a book from conception to delivery. How many pages a week are you going to deliver? Will it always be the same number of pages? Will your quality suffer just to get the next installment out?
Consider a long fantasy, like the first Harry Potter: 384 pages. If I could finish writing that in 9 months; which is 39 weeks, I would be delivering 10 pages per week. Or about a chapter per month.
I finish a book like that in a weekend. I would not read a book in that fashion over nine months. It would be too disruptive to my reading immersion; I would forget too much in-between installments and have to re-read old material. So, even though your writing might be something I want to read, you would lose me as an audience member quickly.
Even if I wrote the whole thing before I began marketing, so I could deliver installments quickly, sooner or later my writing productivity will catch up with me: If I don't finish something new to sell, I lose the audience.
I am NOT skeptical that giving something away for free is a good way to build an audience; that seems plausible to me. In marketing, a free sample worth 25 cents will be taken and used about 100 times more often than charging 25 cents for the sample. That is basic psychology.
So it is possible, if you had a finished book, you might be able to give away the first ACT (about 25% of the book, ending on a serious note of "what happens next" or "how does this turn out" or an actual cliffhanger if you have one) as a free sample, and have immediately available the rest of the book for some reasonable price, and let the readers know that up front.
If I know I am reading a free sample and won't get the whole story, but the whole story costs $8 or whatever a paperback usually costs, I'm willing to make my judgment on the first 60 pages or so. That is more than I get in a bookstore; I will typically read (for an unknown author) about five or ten pages before I make a decision to buy, and my decision to buy is basically "Did I want to turn every page?" If so, it is well written, and I don't skip ahead.
Of course integral to that decision is they did get it published, so I still have a small amount of trust in actual publishing houses, that the opening is not the only good writing in the book!
For a self-published author, I'd guess that 50-60 pages of good writing is worth paying for the rest of the story. In the first Harry Potter, Hagrid first appears at the end of Chapter 3, page 56. So you want to read Chapter 4!
That might be a route; and it can be marketed in that way periodically forever. Like I said, it is just an extension of what happens in a brick-and-mortar bookstore; and to an extent what Amazon sometimes allows in "preview", and free samples are good marketing practice.
You can do much of the work to support this mode of operation before you finish the book; like figuring out how to produce your book for sale on iTunes, or building yourself a simple website and be able to take payments.
But I wouldn't start marketing a book, even free previews, until your book is finished and in your eyes ready to sell.
I will remark that finishing the book is free to you, and if you truly intend to be a profitable author, waiting until you have a finished book should not delay any profits you will reap by very much, and it will not put you on deadlines which can lead to substandard work and a loss of audience. While you are promoting one book, you can be writing the next, at your leisure. You can also build your email list (require an email address before delivering anything free). Even if they don't buy, you have a list of people intrigued enough by your pitch or ad to get the first ACT. You may be able to have conversations with them and ask them if they liked the first ACT, or if there was a reason they did not buy the rest.