It's unlikely, although you might get the odd plant that comes true, but you won't know that until you eat them!

They usually breed true, unless they are hybrids, I haven't checked on Jasper. The main problem is getting them to germinate in the first place. As the liquid/jelly that surrounds the seeds contains a germination inhibitor, if you don't want them sprouting about September (lol) then wash them well.

'Violet Jasper' is an heirloom variety, so it should come true from seed, unless it was accidentally pollinated with another variety.