I've done a lot of crown and I always cope my inside corners. This way you never have to worry about the angle.
Outside corners, yes, you do have to adjust for the angle if necessary.
Another option that is even easier is to use corner blocks, specially made for crown. Although not necessarily authentic, they do look good and all crown is just cut square. That was one of the fastest crown jobs I ever did.
Corner blocks come in various styles to match your crown. The last ones I used were synthetic Fypon type material.