It is an excellent idea to have your paralegal send a welcome letter to a new client as suggested by Dave Swanner at South Carolina Trial Law Blog. As Dave suggests, it is a good way to let the client know who they can reach in case the lawyer is unavailable or even if they just have a question they need answered.
The only issue I would take with his suggestion is that the paralegals letter should be IN ADDITION to a welcome letter from the lawyer. You would not want to send the message that the lawyer is already too busy to welcome them to the firm. Anyway, two is better than one, so I would do both. The client will be doubly pleased.