yes, it will produce seeds but don't expect the plants from them to look like the parent. Dahlias don't come true to the parents from seed- only from tubers.
The seeds look like flattened earwigs :)

The seeds are just amongst the dried petals, correct?

At what point can I pick the seed heads? Just when they're browning?

BTW, looked at the package this morning and they are Unwin Dahlias.

Unwins dahlias are dahlias that were developed many years ago to be grown from seeds. There are a couple of other types including the coltness series. They do make seeds and if you like what you grew this year, your seedlings will look about the same, assuming you grew no other dahlias nearby. Seeds form in small pods after the petals fall off the flower. It takes about two weeks for them to ripen after the florets fall off. These varieties do make some small tubers that can be dug and stored also. Having said all of that, these bedding varieties are quite inferior to modern dahlias. If you want bedding dahlias, look in the nurseries for small bedding types grown from cuttings. Two of the series include Karma and Gallery, both developed in Holland. There are also new dark foliage types from New Zealand that are quite nice. You will 10 times more satisfied with these bedding dahlias than any you can grow from seeds.