Yes, native and non-native plants(AKA weeds) will move in. I don't know how rural your neighborhood is, but many towns and cities have laws regarding the height of weeds.

I have a small mulched area in my backyard where we let some native grasses, mostly panicums, grow for the birds. A blue-eyed grass showed up this year! However, the area is not completely covered. The birds appreciated the dried old leaves this spring when it was time to build nests. Lots of species stopped by for supplies.

I think there are so many introduced species in any given populated area that there is little guarantee that native species will become dominant.

An Impromptu Meadow:

My landlord, lax about mowing last year after they moved into town, has come out to mow exactly twice this year. Now, claiming the mower broke he hasn't been seen since July 1st. The grass is over a foot tall in places and has become a haven for thousands of grasshoppers. Walking through it creates sort of a reverse wake as the hoppers leap away. For over 6 weeks, the lawn has been growing a crop of grasses, wildflowers of various sorts and a small forest of trees. Some fast growing trees were over 2 feet tall awith stems up to 1/2" thick. I spent this morning cutting them all down with the hand pruners since it's obvious I'm going to have to buy a mower and maintain the lawn.

(End of rant.) The point being you will likely get more than a meadow if you don't keep on top of the trees that may sprout. You might try leaving a few smaller spots unmowed to see what species become dominant before committing a large area.

Wayne in the Adirondack Prairie lands.

A large percentage of the native grasses and forbs that was the landscape before white men came here have been eliminated by overgrazing, row cropping, and the introduction of aggressive non native cool season grasses and forbs. While a few places do retain some native plants,
in most areas there is no remant of most native plants and no seedbank left to reestablish a native landscape.
Typically, to restore an area to something resembling its original native state,seeds or plants must be reintroduced and the aggressive, invassive non natives must be systematically eliminated.
Nature will take its course, but first we need help her to undo the damage we have done over the last 500 years.

There are some very good prairie pages to look at, some more intensive than others

No, you won't get a pretty meadow. The climax ecosystem in the east is forest. You get grassland--prairie.meadow, whqatever you want to call it--as the climax only in drier areas, such as the midwest and west. If you stop mowing a patch of lawn in the east, you will first get tall lawn grass and weeds, with some desirable forbs such as goldenrod. (You may also get a summons if your town has weed laws, as mine does.) Within a season or so, you will get woody growth from whatever seeds the birds plant. In other words, the trees that appear will be whatever is nearby. If it's native species, you'll get native species. If it's aliens, you'll get aliens. But within a few years you will have a thicket, not a meadow or prairie. And a few years after that you'll have a forest.

I suggest you look at a good ecology primer, such as the Peterson's field guide series book about eastern forests, to understand forest succession. Sarah Stein's book Noah's Garden does a very good job of explaining what a prairie is and why it's not just a lawn grown wild--your is a very common misconception. Prairie Nursery in Wisconsin has an extremely informative catalog that explains how to plant and maintain a prairie.

What Elaine describe's is pretty accurate. I maintain a "meadow" area on my property, "maintain" being the key word. Once a year I go through it and cut out any tree's or other undesirables (Japanese honeysuckle especially.) It ain't pretty, but it's good for wildlife. It does have a variety of sporadic wildflowers which I sometimes transplant, though it is mainly overgrown tall fescue.

I do have a low lying area that has been taken over by Marsh Bulrush and some other sedges that is quite nice.

Look at the areas under major power lines that are mowed periodically by the utility company. Those are an example of what you can expect to appear without serious maintenence.

Not digging is important. If you did till, you'd bring up all kinds of weeds, which would quickly outcompete any natives that were at the site.

I know a few people who have meadows, and none are effortless. One person stopped mowing or burning a field and started weeding it instead, and the natives came back. That was quite a few years ago, and it still requires lots of hand-weeding.

Another person removed a lawn and planted native bunchgrasses and annual wildflowers, then took them all out a year later because the bunchgrasses were too thick and would have become a turf, and replanted with less invasive grasses and perennial wildflowers. Perennials are less work than annuals, usually, but not as showy.

Someone else has been collecting local native seed and trying to restore a hillside, but the germination rate seems low (more like nature than like a garden, in other words), and progress is slow. Occasionally the deer get in and eat some of the plants.