You can give it a try. I'm sure the product is as presented, which is to say, they're giving you a quality seed mixture, and it will grow.

There's only one problem, but it's a big one:

You can't grow turfgrass in the shade.
You can't grow turfgrass in the shade.

Now that we have the basics down, we can start looking at the problem right-side-up, rather than looking at the problem upside down.

There are a few grasses that can tolerate partial shade, for part of the day. Those grasses tend to be fescues, and some perennial ryes. The various companies tend to mix them together and call them a 'shade' mix, knowing very well (which you now know) that the rule above will still apply.

My advice would be to buy the product you mentioned, in the absolutely smallest container you can buy. Get the one pound, rather than the five pound, bag off the shelf. Then go to Home Depot, and buy a different brand of 'shady mix'. Then go to Lowes, or Meijer, and buy yet ANOTHER different brand of 'shady mix'. Maybe a fourth stop, and maybe not, to get yet another different brand of shady mix.

Here's why:
Brand One will have

14% Name A Tall Fescue
24% Name B Chewings Fescue
20% Name C Tall Fescue

Brand Two will have
12% Name B Chewings Fescue
20% Name D Hard Fescue
23% Name E Tall Fescue

Brand Three will have
15% Name C Tall Fescue
21% Name E Tall Fescue
22% Name F Chewings Fescue

As you can see, there is some overlap, but now you've got six or seven or more varieties of grass that will tolerate some (but not a lot) of shade. Mix them together, thoroughly, in one of those orange paint 5 gal buckets from Home Depot, or similar dry bucket.

Plant, water, and grow. Every spot there in your shade problem is a little different, as shade tends to come and go during the day, as the sun passes over. And now, every spot of that shaded area has six or seven different grasses that might grow there. You have planted them all at once. One of those varieties will like the spot better than others, and (we already know) at least half of them won't like the spot at all, and won't grow. We're hoping that something will thrive there.

As to some spots, nothing will thrive. That is not your fault. You know the rule: You can't grow turfgrass in the shade. You gave it a heck of a shot, but the fact is, that spot won't support turf, as it's in the shade.

So let's look at the problem right side up: let's decide whether we can thin (I prefer 'thin' to 'remove') nearby trees to create LESS shade in those problem areas. A tree service can give you advice how to thin the tree while still keeping a tree good looking, and there are some trees that just aren't worth keeping, when looking at the lot overall. You have to make those decisions. But you're looking at the problem the right way: the problem isn't you, and it isn't the grass seed.

As to those areas where you prefer (for any of a lot of reasons) to keep the shade, talk to the same tree service: they can bring you a load of wood chips, which can be spread in those shady areas, and look quite nice.

It has a blend of DaVinci Tall Fescue, Rembrandt Tall Fescue, Masterpiece Tall Fescue, and Picasso Tall Fescue.

Here is a link that might be useful: Greenview Fairway Grass Seed - Shade Mixture

Those are all great varieties, and tall fescue is known to tolerate shade but not deep shade, so the answer depends on how much direct or filtered sunlight the area receives. I would think you need a few hours of sunlight at least. For less sunlight, you need a fine fescue, which is known to tolerate shadier areas. And, there are Philes comments to think about. But because the fine fescues are most likely to grow in shade, the biggest problem isn't that trees obstruct sunlight but that they compete with the grass for moisture and nutrients in the soil, and they always win. So, if you can't even get fine fescue to grow, then trimming trees won't be the solution either.

Mogo,
You use this seed in your sunny areas, too???
Miss Mary

I have also used it in the sunny areas. Though it was slower to come up there, but now with this lovely rainy weather I think it will sprout better.