Hint: the answer is not really. But maybe a little bit…
After doing a blind tasting with two yellow cakes, one made with cold eggs, the other with room-temperature eggs, the panel concluded that the difference between the two cakes was negligible.
The cake made with room-temperature eggs had a slightly finer, more even crumb, but the cold-egg cake was entirely acceptable. Overall, tasters strained to detect differences between the two cakes, so it’s fine to use cold eggs in most basic cake recipes.
via Do Cold Eggs Really Make a Difference in Baking? | The Kitchn.