To retain the characteristics of a cultivar it is usual to propagate it vegetatively by cuttings or division, thereby creating clones. But if I isolate a plant that will self-pollinate, will the resulting seedlings be true to the form of the parent and will it be taxonomically correct to use the cultivar name for these seedlings?
I think the answer depends on the taxon being grown, but generally the offspring will not be the same as the parent. Some plants are simply self infertile, so nothing would result from those taxa. Some plants produce apomictic seeds--these will produce direct clones of the parent without actual fertilization. Some of these may also produce pollinated seedlings--so you would have to watch for that. There is also what are called stable seed varieties. This is what you have with annual seed varieties. The breeder has continually selected for particular traits over enough generations to "weed" out the unwanted genes until the strain is deemed to be stable.