You can, but we’re not sure it’s worth it. Yolks don’t take to freezing very well. They become very gelatinous and you usually mix separated yolks with a bit or salt or sugar before you freeze them to keep them from turning to rubber (and you label them well so you don’t have to guess if you mixed them with salt or with sugar). Raw egg whites do not suffer from freezing (cooked egg whites are very rubbery after freezing).

If you’re going to freeze whole eggs, remove them from the shells, and mix them well before freezing. They can be kept frozen for a year, and should be thawed in the refrigerator the day before you intend to use them. You might try freezing a few eggs and see if the results are acceptable to you.

Purchased from a busy store (that has lots of turnover), stored in the bottom of the refrigerator (where it's colder), not in the door (where they are subject to more temperature fluctuation), eggs should remain fresh for four or five weeks from the date of purchase. That comes out to about two eggs for each of you each week. That doesn't strike us as an unreasonable egg-consuming quota. You can probably skip the freezing step, and if you become concerned about freshness, you can bake a cake once a month or so to use up any lingering eggs.