Double check the details of those two email accounts, if the logins are the same, it should be safe to remove one.

Check out the email rules (Tools > Rules and Alerts...), they control where to store each email, they probably do other things as well, examine one by one, if you understand what they do, you will know if it's OK to remove them.

BTW, Gmail is great. I would use Gamil's web interface if it's OK with my employer.