I've rooted several Monstera Deliciosa cuttings in the past and can't say I remember just when the first roots appeared or what they looked like. I was so busy with other things that I neglected them except to keep water levels topped up. When I finally made time to pot them, months later, they had masses of long whitish roots and were non the worse for having had a semi-aquatic life for longer than you would usually expect to keep a cutting in water.

I'll be taking quite a lot more cuttings as soon as I have a greenhouse (this spring.) in my old house I had two modest sized monsteras either side of the fireplace, They came with me when I moved house nearly 15 years ago, and I placed them either side of the doorway into a very sunny living room. They are now floor-to-ceiling indoor "trees", but the house wouldn't be home without them. I'll have to take cuttings now that new leaves are rubbing the ceiling.