Indexing on a field which is in array of subdocuments

I'm trying to figure out the best design for the messaging system I'm porting from SQL Server to MongoDB - currently (in SQL Server) there are tree tables that store the message: Messages, Inbox and Sent. The message is stored in Messages table, and Inbox/Sent have entries for all recipients/senders for each message.

Now, in MongoDB I wanted to combine those three into one collection, with documents like this:

{
    _id: 
    subject:
    body:
    sender: {memid:, name:}
    recip: [{memid:, name:}, {memid:, name:}, {memid:, name:}, etc]

}

Now, I need to be able to retrieve all messages for a given recipient by memid and I have to do it fast, so an index is required (I will have hundreds of millions of such entries). So, my question is - can I index by a field of a document in an array?