No, it’s not relevant. Seriously, go consult a lawyer in this. I have. They’re very consistent on this point because there are tons of case law regarding it.
There are a massive number of examples of patent and copyright litigation stemming from work done for one employer, who rejected it, then the employee goes off and founds their own company and gets successfully sued.
Fairchild was unique in that they had claim to the IP that their employees wanted to use in new startups, yet they decided not to follow through and allowed the employees to start their own companies. They could’ve prosecuted but didn’t, and as a result we got Silicon Valley and the culture that surrounds it.
But it’s no guarantee that that your employer won’t pursue a copyright claim they are perfectly within their rights to do. Don’t assume your employer is Fairchild.