You would think so, but it won’t let your companions lay more eggs when you’re at the limit. This is separate to the companion slot limit. I assume it doesn’t let you redeem eggs when you’re at the limit either.
If I had to guess, eggs require more data than a typical inventory item, due to the complexities of creatures. They’re probably implemented differently with some hacks to make it work, and limiting numbers is the simplest way to avoid complications.