When you use this function, if the 'friend' is a member here, does their account show that the book is on it's way to them? And so can they mark the book received?  Or is it the same as if we have a book sent to a non-member friend or relative and we must mark it received when we hear from them that it has arrived?

I haven't done it for awhile, but I seem to remember that the "friend" doesn't get any notice of the transaction. You can send them the tracking number and you can mark it received when they let you know it was received.

Amber is correct and that’s how I do it too. Many times it’s an extra book from a book deal so they let me know when the package gets there.  When I use it for games I wait for the member’s post in the thread & then mark it received.

I use the "Mail To A Friend" feature all the time when I do Book deals - it
1) Removes the title off of my bookshelf without me having to do it myself 
2) generates a complete list of all the books I am about to mail for use as a package contents for the USPS for varios reasons.
3) creates a Mailed to a Friend Tab on my Main Page. detailing each title sent

PBS will send a "reminder" after a set time asking if your 'friend' had received the books or not
You will have to acknowledge that the books (each seperate title) were received so that they may be removed and accounted for.
It's a wonderful feature and can be used to send 'books' to members and non-members alike.