Do you think this would work to give a faux finish?

It will certainly give you one heck of a mess, faux finish?, that I guess it would.I do not think mixing paint with JC is a good idea, applying such with a spatula, certainly not a good idea. Think about what you are going to do and how to repair it once done.

Your goal is to give a faux plaster finish, I take it. It would be easy enough to try. Get a piece of drywall at a hardware store and try it.

Any kind of water-based wall paint should work.

Personally, I would not want to buy a house where this had been done because getting the walls back to flat would be a lot of work, akin to removing popcorn texture from a ceiling.

What you say makes sense. So since the walls have just been painted, many defects show through, the patchwork is not good and stands out, what is my next step?

The technique you are talking about works, but I agree with graywings about it semi-permanently changing the surface of the wall. It's pretty expensive to refloat a wall to flat. If you want some special finish, try troweling on high quality (thick) paint (instead of the tinted mud). Not sure what you want the overall effect to be is, but it does work. And can be really spectacular if done right. (and painted over if done poorly.)

What you say makes sense. So since the walls have just been painted, many defects show through, the patchwork is not good and stands out, what is my next step?

Fix it properly or hire someone to do it. It is not that hard to do

Both painters told me that the walls had many holes in it, they are old, and that sometimes they simply cannot be restored to a uniform flat surface. Both painters are experienced. I just wonder what to do now, where I am going to find a good painter. If I could figure how to skim coat and it's not that difficult, I might do that. Or maybe I could really just get drywall and have somebody replace the old drywall.

cindi, if you do a test board, try this as well: trowel on regular untinted sheet rock mud/joint compound. (maybe water it down a little). Don't worry too much about skipping around. Let it dry. Do it again concentrating on creating a second depth and reaching other places-exposed bare wall in places is fine, that will be another depth layer. Kind of rugged but pretty. Paint it, then GLAZE it allowing the tinted glaze to seep into the cracks and crevices. Use a light hand or a heavy hand on the glaze. I like subtle personally.

A painter may not be able to get your walls back to a uniform flat surface, but they should be able to get them back to something that you can happily live with. I live in an old house and the walls are far from perfect. Don't try to learn to skim coat. Hire one of those painters and tell them to do what they can to improve the walls.