The whites - yes, definitely. The yolks can be frozen, but they take on a different texture after freezing.
Excerpt from an egg company:
" Egg whites
If you have left over egg whites from a recipe, don't discard them. Egg whites can be easily frozen and thawed for future use. For easy measuring when you next need them, first freeze each egg white in an ice cube tray and then transfer to either a freezer bag or container.
Once thawed, whites will beat to a better volume if allowed to sit at room temperature for about 30 minutes.
Egg yolks
Freezing egg yolks is not as easy as freezing egg whites as the gelatinous nature of the yolks causes them to thicken or gel when frozen. To help retard this, beat in either 1/2 teaspoon of salt or 1 1/2 teaspoons of sugar or corn syrup per 1/4 cup of egg yolks (approximately 4 yolks).
Ensure you label the yolks according to whether they were mixed with salt or sugar so you know whether to use them for savory dishes (salt) or sweets and desserts (sugar)."
I know because this dish has an egg yolk that has been frozen and then thawed and it has an interesting texture: