Hi ,
You can create a single dynamic distribution group with the condition to have only the mailboxes in exchange as its members . Then when a person send an email to that Dynamic distribution group it will get distributed to all the mailboxes
in exchange.
Note : Most important feature in the dynamic group is that the membership of that group will be maintained automatically and also along with that we can have group membership by defining the recipient types/OU /rules.
I agree with ED and also based on my knowledge you cannot achieve your scenario without Distribution groups or dynamic distribution groups.