You can do this with a mailing list instead of an alias, and limit who can actually post to the list that way.  You can set the list to allow anyone to post, subscribers only to post, or moderator only to post.  If you allow, for example, only subscribers to post, you can then enable the poster whitelist and set only the ones (selected from the subscriber list) allowed to post in that list.
 

Adam, another option that I have tested and works is to create a domain content filter using "From specific addresses" and "To specific addresses" as the filter options. In the "From Address" set it to "Does Not Match" and enter the addresses of each manager; in the "To Address" set it to "Matches" and enter the alias address.  Then choose the appropriate action to perform if anyone except managers send to that alias (e.g., delete message).