like all other plants, if they are not pollinated they won't seed - just like if peppers are not pollinated they won't fruit, of course nasturtium doesn't produce fruit.
how do i know, i grow nasturtiums and have grown them for years. i grow them for me and i grow them for neighbours.
in the morning i will take some pictures.............if i remember i responded to this post.
for whatever reason nasturtium are not the favourite flower of bees, you will most likely have to pollinate them by hand. Reds seem to attract insects, followed by yellow. orange can't attract anyone to pollinate them.
the nasturtium is a beautiful plant with its large clover leaf like leaf and the umbrella like flower. as the reds die off the flower turns purple, yellows are brilliant and the orange variety are pastel. you can eat the leaves(they have a peppery flavour) and the flower.........i have never tried the flower - nor would i try the flower of a zucchini plant or any other flower.
nasturtium pollin does stain, i have found yellow the biggest stainer.
i grow them both in containers and in ground and always use tomato rings to let them climb and collect their seed.
i hope this helps; good luck with your nasturtium growing.