Seedless oranges and seedless grapes are the result of cultivation of naturally occurring seedless plants. The navel orange is descended from a seedless orange tree which developed through natural mutation, that is, something in its genetic material had spontaneously changed, resulting in this unique plant. The common supermarket green seedless grapes Thompson are descended from a European seedless grape strain that probably originated between the Black and Caucasus Seas. The Thompson has a genetic abnormality that causes the seeds to arrest development. Though the flower is pollinated and the ovum fertilized, the seeds stop growing after a few weeks. So, the grape is not entirely seedless; rather, the seeds are aborted, and exist as tiny specks inside the fruit. Commercial growers treat the plants with a growth hormone called gibberillin, which is normally secreted by developing seeds. The flowers are dipped or sprayed with the hormone so that the grapes grow big and juicy despite the arrested seeds. Seedless watermelons are sterile, that is seedless, because they have three sets of chromosomes. This condition is called triploid. To produce triploid watermelons, a diploid parent is pollinated by tetraploid watermelon, which has four chromosomes.

Read more: http://www.madehow.com/Volume-6/Seedless-Fruits-and-Vegetables.html#ixzz50RvZNXdf

Seedless fruits can develop in one of two ways: either the fruit develops without fertilization (parthenocarpy), or pollination triggers fruit development, but the ovules or embryos abort without producing mature seeds (stenospermocarpy). Lacking seeds, and thus the capacity to propagate via the fruit, the plants are generally propagated vegetatively

So it is more likely that one can propagate plants vegetatively from plants with seedless fruits than the other way around imo :).

Yes , there is very much a strong possibility to have naturally evolved seedless plant type , especially in cross pollinated fruits crops , which happens because of the natural mutation over a period of time. We normally coin such identification of plant as clonal selection . In perennial fruits , most of the varieties , instead of being bred , they are simply the clonal selection due to chance mutation. However, it remains to be seen, how long natural selection in cross pollinated crops , seedlessness sustains..? Dr Malhotra is the right person to toss up some fascinating response...