Store cracked eggs for a week?
Fine, you're crazy. There's no time savings in shelling a lot of eggs at once .vs. shelling them as you need them, and there is a HUGE loss of storage life.

Once removed from the shell, 2-4 days is the official word, so a week - no.

http://www.foodsafety.gov/keep/charts/eggstorage.html

http://www.incredibleegg.org/cooking-school/tips-tricks/egg-storage/

The first site suggests the possibility that you might beat them and freeze them, but then fails to give a storage time for that particular option. The second site suggests that up to a year is acceptable, and further suggests adding salt or sugar to improve the texture of egg yolks that have been frozen. I have no practical experience with freezing eggs myself, they last quite long enough in the shell in my refrigerator for my purposes.