The disturbance of soil will expose dormant seeds. You may find new types of weeds sprout along with a lot of dandelion seedlings. The old, broken roots may take time to regrow-you could see them next year.

So, getting your new grass seed it grow strong is very important. Fall is the best time to start, as you have planned. I bet that you will have to deal with weeds after it grows like everybody else!

How long a dandelion may take to regrow from a piece of root depends on how deep in the soil that root broke off. Sometimes you will see new growth in a week and other times maybe not for a couple of months.
Between now and when you seed in the fall take a good, in depth, look at this soil. Have a good, reliable soil test done for pH, P, K, Ca, Mg, and the ratio between them and then use these simple soil tests to see what else you might need do to make that soil into a good, healthy soil that will grow strong and healthy plants that will be better able to crowd out any "weeds".
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains� too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.