Yes it’s possible, but I would suggest a different approach. There is no need to replicate the relatively large Domino directory. In addition to people’s Email addresses, It contains server documents, config docs, certificates and many other types of documents needed by the server and completely useless to users.
Instead I’d suggest created a “Condensed Directory Catalog” (CDC), also referred to as a “mobile directory catalog”. It’s quick and easy to do. Look up Condensed Directory Catalog in the Domino Administrator help database. Now to automatically create a replica on everyone’s computer, create an organizational policy, and a desktop setting document to push a replica to everyone.
You would only want to push a replica to everyone if they are on laptops or have poor connectivity to the server, otherwise there is no need to push a replica to people.