Highly unlikely. Her private server existed years before Trump declared his presidential run.
I remember one time my father forgot the password to UNLOCK his laptop. I got on the internet and copied a password hack program onto a CD, booted from the CD and VOILA! I accessed his laptop and told him what his password was!
Also, how did Petraeus share info. with Paula Broadwell when they were apart? Simple. He gave her his username and password so she could log in to his email! No surface mailings required. She would just log in to his account and print stuff out.