Hello Molly,
I have grown, Pelargoniums, Hardy Geraniums and Erodiums from saved seed. In the case of Hardy geraniums and Erodiums the seedlings were indistinguishable from the parent plants. I have also collected seedlings from around these plants that were self sown. In the case of pelargonims, they are actually half hardy perennials, I have grown two or three different named varieties from and found the to be identical to the parent plant. I have not attempted to hybridise any of these plants
I would suggest that, if space permits, you lift your plants and overwinter them in a frost free environment as well as sowing your saved seed.
Ron