As part of a body weight circuit, I have been using the plank as the abdominal component. Additionally, I have been working on doing handstands, in preparation for doing handstand push ups.
Currently I am doing wall-assisted handstands, but I will progress to free-standing.
Handstands are mostly skill work, rather than strength work (other than right at the beginning) -- you are learning to balance, to make small adjustments in order to stay upright. Therefore, it cannot replace the plank. If you are looking for ab specific work harder than planks, consider ab wheel rollouts or L-sits.
Additionally, you'll want to do handstands before strength training, so that you are as rested as possible. Generally, one would set a timer for 5 or 10 minutes and do as many handstands as possible, rests included in the time; alternatively, spread out during the whole day. Daily handstand work will also allow for more progress -- skill work should never be too fatiguing. For more information on handstands, check out this thread on Reddit.
I'm a handstand noob. I find that my wall-assisted handstands involve my abs to a lesser degree than planks even with good form (tight glutes, abs, straight trunk). With handstands, I find it much easier than with planks to fall into a cheating position where I'm not contracting my abs. I do not find my handstands to be a tremendous ab workout and when concerned with my abs I do other things for them.
It doesn't. Handstand has very little to do with abs. Proper handstand has VERY little to do with the engagement of any muscle group. By proper I mean perfect handstand - extended elbows, straight body. But even in an imperfect handstand I doubt you can feel the abs working at all. I never did feel them, even in my beginner handstand days.
Considering the aforementioned - no both exercises are not replaceable in the essence of your questions.
