Leslie & Adam,
Here is a link to a pdf of the Brother manual for their newer model 7840 that I am considering for our place. As I remember the manual for many of the older models like Leslie's (I read it a while back) the set up and use was pretty much the same.
As you can see that computer that recieves the faxes needs to be on to actually get them, but the printer has a pretty good amount of memory that should hold most of us over for a weekend if we care to turn off our computers. Hope this helps...
http://www.brother-usa.com/ModelDocuments/Consumer/Users%20Manual/UM_MFC_7440N_7840W_EN_1450.PDFPaul
