This project is definitely possible! However, the only way to use the Gmail interface does have a monthly cost associated with it (€4 per user per month). There are other options, that do not have this cost associated with them, but the interface will be slightly different. They may also not offer as much storage as Gmail do.
As for my personal experience, I have set up a Gmail interface with a personal domain for a family member before. Although I am currently near Berlin, I am going back to the UK soon, so would most likely have to do this project remotely, which is perfectly possible.
If you would like to contact me to discuss further details, please do.
Thanks, Sam.