The best and easiest way to do this kind of testing and to get rid of this issue is to have a test email ID like 'DemoTest@domain.com', and use this email ID for your and developer's testing purposes, i.e. where ever in system you need to enter the email ID use this one and proceed further, by this way your problem of mail bounce will get resolved regardless of any person is in company or not, this email ID will always remain active. Secondly, you can keep credentials of this email ID with you (QA person), Developer (Technical Lead) and PM (Project Manager), so that there are no dependency issues. In this case even if anyone of you leave the project or company then your work will go on.
Remember this test email ID can be of your company or any other email provider like Gmail, yahoo etc. But for security reasons I will suggest to have test email ID of your company only this will allow better security of data. you can get one created from client as well, so that they receive such mails from production server.
Another thing you must know that adding personal email ID in code and configuration is bad practice, especially when that code needs to be deployed to production server. At that time, you should highlight this issue as well. As a member of QA team you are not only responsible for bugs and testing but the overall quality and health of the project, which is being hampered by this activity. Make this part of your checklist that either you or deployment team needs to check that there is no personal email ID in application after deployment which belongs to your organization. If there is any, then replace it with your TestDemo email ID.