It can still be e-filed.  Just make sure you enter the date of death for the deceased spouse, PTO will put the header on the return and the notation on the signature line.  You may, however, be prompted to make an entry for the c/o address.

Can they e-file the NJ return also or must it be mailed in since NJ requires a copy of the death certificate?

NJ allows the return to be e-filed and only needs a copy of the death certificate if filed on paper.  Your client just need to ensure the death certificate is available upon request assuming you will e-file the return.  Having said that, I would attach a copy with the e-filed return.