Yes and no…
Most of the time the size of the eggs you use doesn’t make a difference EXCEPT in baking, where measurements matter.  Even then, if your recipe calls for just one, or maybe two, eggs You’ll probably be ok in the difference between a large and extra large egg.   ( I don’t even mess with medium eggs)  BUT , the larger the number of eggs the more size matters.
It takes about 5 large eggs to make one fluid cup, but only 4 extra large. So, in baking, using the wrong size egg can affect the texture and consistency of your recipe.

Large                             Extra Large                      Jumbo
3.5 tablespoons           4 tablespoons               4.5 tablespoons
4 eggs = 7/8 cup           4 eggs = 1 cup              4 eggs = 1 1/8 cup

So, you see, there’s about 1/4 fluid cup’s difference between 4 large and 4 jumbo eggs and that difference CAN matter.