It sounds like he doesn't want to force a work email account on his employees. I don't think many people would have a problem with a work email, it's the norm after all, but fine.
But he also doesn't want to add their personal email addresses to his address book (is this why he wants the @dnalounge.com addresses?)
I'm not sure what this setup is attempting to accomplish.
Actually, makes sense, because he can then save those emails on the server, back them up, and they'll be in his control if an employee ever leaves. It's good corporate policy. I believe the White House is having a similar conversation lately.
So again, I'm not sure what problem he's trying to solve here. To be clear I'm not saying he shouldn't be able to set up his email this way and have it work, just that I don't get why he WANTS to do it this way. What is it accomplishing?
Especially since you can configure gmail to serve as an interface to arbitrary third party POP3/IMAP services.
"This would work but I'd rather find a more elegant solution" seems like a perfectly reasonable desire to me.