Most likely not. Do you know the species by chance though, and do you have more than one? I know at least some sea hares are hermaproditic, but they’re not self-fertile and to my knowledge they can’t store sperm to fertilize eggs at a later date like some animals can. So, if you only have one the eggs are probably not fertile. Plus, even if they are fertile, the sea hares I’ve looked at have planktonic larvae - so they’ll be eaten or pulled into filters, killed by powerheads, etc.
If you want to raise them, you’d almost certainly need a growout tank setup for that purpose.