I did this. I had a 170,000 word novel, which is crazy long for a contemporary romance, so I broke it up and published it as a serial novel. There will always be some people who complain about serialized novels, so you have to expect that in the reviews, but I was very pleased overall with how my serial novel was received.
It started out rather slow but started to pick up steam in sales after the fourth volume. The last three volumes were in the top 100 on Amazon the day after they were published. I
bundled all the volumes afterwards, and naturally that is the title that has sustained sales months afterwards. I did a BookBub promotion with the bundled book shortly after I published it (which they accepted even without reviews because of the high reviews on the individual volumes) and made the USA Today bestseller list that week.
I don't think every book will work with this strategy, though. You need to make sure you have a substantive piece of the story with each volume (my volumes were between 20,000 and 35,000 words each). I don't think you need a definite climax and ending point with each volume (my highest reviewed
volume ended with the heroine about to die), but it has to be enough for readers to feel satisfied that the story has genuinely moved along. Each volume needs a turning point at least.
And a couple of things you must do to really pick up momentum with a serial novel. First, you need to put the schedule in the book description, so readers know exactly when to expect the next volumes, and then commit to publishing on the schedule. Amazon got held up for some reason with getting my fifth volume up for sell, so it wasn't available the morning of the scheduled day, and people were stalking my Facebook page, waiting for news on when it would appear. Since it was Amazon's slowness and not mine, they were completely understanding, but you definitely don't want to lose the faith of readers by not following your publicized schedule.
And then--and this is the hardest thing--you need to give readers a reason to pick up the first volume. Asking readers to pay $.99 for one little piece of a novel (when they can get an entire book bundle for $.99 now) is a really hard sell. I put the first three volumes of mine on Kindle Select, so I could offer them for free, and that's really what got the serial moving. Readers could try it out with no risk, and then they were hooked and didn't begrudge spending $.99 for the three remaining volumes. I'm sure there are other ways to get readers to start reading, but this is definitely the biggest hurdle.