If you work full-time for a large Fortune 100 company and register a Delaware corporation, will your employer find out about it? Obviously there is some public record, but is this something easy to find, or something companies commonly look for?
Unless I'm missing something, you are not owned by a company and can incorporate.
Incorporation is different than competing against them / violating anti-compete agreements.
Whether your company actively searches for them is unanswerable, since each company is different.
If someone isn't actively looking, they'll never find out about it. There are millions of businesses registered everywhere. They will have to actively look for businesses owned by you (in every state) to find out.
why would they do that?
The Delaware Secretary of State keeps incorporator and officer names hidden behind a paywall. Their online entity search (https://delecorp.delaware.gov/tin/GINameSearch.jsp ) only provides the name and address of the registered agent. One needs to specifically request to purchase a copy of the incorporation documents filed for the entity in order to find out. Delaware performs searches by entity name, not by incorporator/officer name. So your employer would have to know what you named your company to even have a lead. See this for yourself - give the Delaware SecState office a call (302-739-3073) and see if they disclose the name of companies that belong to person XYZ and the details of shareholders. Furthermore, the incorporator isn't necessarily the owner (majority shareholder) of the company, and the name of the latter is not on the incorporation documents.The amount of work, time, and cost involved in obtaining all this information is not scalable nor is it a good use of HR resources.
More importantly, a business entity alone is not valuable intellectual property for all practical business purposes. Of greater concern to employers is the intellectual property you own (e.g. patents, trademarks) that may compete with theirs.
Even if they somehow found out, simply founding or being a part of another corporation does signify any type of "outside venture" or whatever is defined in your employee handbook. The corporation could be a holding company for real estate, or your wife incorporated her business and listed you as a cofounder.
Companies write these clauses into their handbooks to prevent employees from competing against them, and to ensure you any outside work is not affecting your performance i.e. working on your venture during working hours.