They can try all they want.
It all depends on who they happen to be, and how you define an Easter Egg.
I worked in games for many years and we included quite a few Easter Eggs. But they were not hidden from the studio. They were approved by management, tested by QA, and documented internally. We tried to keep them quiet to see how long it took for them to be found.
The article is right -- large corporations that are risk averse tend to crack down hard on undocumented Easter Eggs. I think that is correct for a business, to crack down hard on undocumented, unapproved, untested features.
The key detail is who knows about it, and how appropriate it is for the product.
Critically: Did it get approved and tested, and is it okay for the user? An Easter Egg that has been approved by designers and product managers, tested by QA, and is a happy surprise to the user is a good thing. If it was not approved, but the programmer intentionally threw in the feature without testing and without documentation, yes, the business should crack down.
The trickier ones are the ones that are approved and tested, but not quite what the customer expects. Microsoft's bouncing text screensaver used to have an Easter Egg that typing "volcano" for the text caused a cycle of volcano names. Fun, for sure, but if your screen savers were used for the machine name, and the machine name happened to be "volcano", then it is an unexpected negative behavior.
Someone working on Excel, a product used inside government agencies and nearly every major business, including secret unapproved features? Yeah, that's absolutely a fire-able offense.
Someone working in a smaller company, with management approval, adding in a small feature to change the color scheme to red and green on Christmas day? Potentially a fun little Easter egg... unless the user is making a major presentation on that day to group that doesn't respect the Christmas holiday, then better make sure there is a way to turn it off.