Does authenticated encryption add any protection to a signed digital envelope?
I suggest that you look at Signcryption; a short survey appears here, and efficient schemes appear here. Just signing then encrypting or vice versa in a naive way is not secure (especially in the multi-user setting). So you have to do this right. Once you have a concrete scheme, you then have to see what level of security the encryption scheme needs to be. Typically it does need to be CCA secure, and the way to build CCA-secure symmetric encryption is the same as authenticated encryption. (Note that doing hybrid encryption or KEM/DEM, you need both the asymmetric and symmetric parts to be CCA secure.)  However, it really depends on exactly what you are doing. Look at the cited references as a starting point.