Some birds with cross beak can live normal lives and some can't. It all depends on the severity of the cross. The beak will continue to change until they reach maturity so it could be a while until you know if this bird can feed itself. As long as the beaks are kept as short as possible, many birds can continue to feed themselves. We file our cross beak's beak once a week. I couldn't imagine letting it grow for 4 weeks, he'd starve by that time. We use a dremmel-like tool and it literally takes 30 second once a week. Every night I check his crop to make sure it's full. Other than the filing and more attention to him eating, he's a normal 6 month old rooster.
It's a terrible thing and it takes time to know if you're bird will be able to make it, but I've never heard of a cross beak that didn't require having their beak filed in order for them to make it. I've seen a lot of birds where people neglected their beaks until it became too long to cut (blood vessels grew long just like with dogs' nails) and the birds starved or were put down.
Wishing you luck. For some reason, cross beak birds seem to have more personality than other chickens which makes them worth fighting for.
