I wouldn't waste your time. A butt has enough internal fat to keep it moist, and they are typically thick enough that it would take more than overnight for the brine to penetrate.
If you want to get more flavor inside you can inject. Chris Lilly's injection is a good starting point, but most guys cut back on the salt.
3/4 cup apple juice
1/2 cup water
1/2 cup sugar
1/4 cup salt
2 tablespoons Worcestershire
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