Mike,
I think best NOT!! There will still be the emails from her previous relationship(s) in that account, not just yours. Even though you would say to yourself that you wouldn't look, eventually you would succumb to curiosity, .....(and you know what curiosity did to the cat!!!)
It's human nature to want to know more, than what is good for you to know!!...
Best left as it is, ....by far, much safer!! lol!!
David....
PS : Of course you could get Jessica or the 3rd party to erase all correspondence prior to
any of your correspondence to Jessica began... That will work!! ...haha!!