Dandelion seeds appear to be able to mature even if not attached to the plants. However, they do need to be pollinated, so it depends on when in the growth cycle they were included in the grass clippings whether they would become viable seeds. I've not seen an increase in the numbers of dandelions in my planting beds when mulching with grass clippings that also have dandelion blossoms mixed in.

I have wondered the same thing myself. To be safe, we try to do a quick go-through where we pluck flowerheads before mowing when practical.

When I hand-pull dandelions, I put the plant in the compost but put the flowers and unopened buds in the trash. Even with that, I did find a dandelion flower growing from a (dead) plant in my covered compost bin!