Does fat transfer to breast look and feel natural ?

I never wanted to do implant as I did not like the fact that it looks fake and my husband doesn't like the idea of touching fake boobs. Does fat grafting to breast give the same result as breast implant (kind of moves in block when running for ex. ). Does the touch feel exactly the same as natural boobs (given it is fat )? Thanks for answering, I am really looking into doing this procedure.