Whilst you can't ever rule anything out, I can't really see how a workplace can get upset if an employee supplies their work email address for an official form.
What will make it more interesting is if the email address supplied no longer works. Either because you have left that company, or because the company no longer exists. Will the "AI" engines they will invariably be using to run this clown show get upset with a bounceback ? Will you be accused of lying to Uncle Sam ?
It's only a matter of time before this administration hits upon the genius idea of making the governments of people detained by ICE to pay for their incarceration. (After all Mexico had to pay to build that wall).