I don't think I did enough demoing as a beginner/intermediate to remember if it would have done me any good before making a purchase. It can't hurt to try though.
I do agree with having a pattern and evaluating for the same sorts of things. I have a route that I use to demo skis that involves traversing, bumps, crud and groomed, where I make a few large radius high speed turns, short turns, and then have a steep open groomed area that I practice a skidding drill and throw them sideways, changing directions a few times, and then set them on edge again to get a feel for how easily they break loose and hook up back into a carve on demand.
And then I go in and grab a different ski every two runs (unless it's something I can tell I hate after a single run), and write down my notes on what I liked and didn't like about each ski in each situation.
And sure, you can just grab demo skis and go and do whatever and buy based on how you happen to feel about them overall, but I know I end up with preconceived notions about some that look nice, or have a great reputation, and breaking it down to give them a rating in the different areas I look at lets me get rid of that and make a more objective choice. I mean - my I.M.88's aren't sexy looking. They were probably my least favorite topsheet, but damn did they feel good, so that's what I bought.
OTOH - I bought a pair of Praxis skis that I haven't demoed. I demoed Spatulas a few years ago and they were super fun, and then the Praxis came out with their cheap pre-order deal, and I figure they should be similar but much lighter in weight so I went for it. It's a quiver ski - if I somehow hate it - I'll sell them. No big deal.
And I do generally feel that powder skis are a problem to demo. First of all, conditions are constantly changing - unless you had a storm day where it's free refills all day, a bluebird powder day is tough. You have a couple runs where it's fluffy, but the sun starts to change the consistency, not to mention how you're skiing more tracked out snow as time goes on. It wouldn't be fair to the skis later in the day to judge them in different snow. Not to mention the biggest problem - how to tear yourself away to go get new skis... or risk skiing something less than ideal in great snow! ;) So honestly, what I end up looking at with powder skis is that assuming they have decent characteristics for a powder ski (width, flex), I still need them to be manageable on groomed and in crud, so I demo them just like regular skis to make sure they work for that stuff too.