Yes, almost always no problem. If you are lucky, the FAX machine will have
dual telephone jacks to allow you to chain another device on. If it does
not, most stores (almost any retail store) sells splitters (2 device up to 4
devices or more) that plug into the outlet. This are a single piece small
splitter. These are relatively cheap, at Dollar stores they go for a couple
of bucks. At Radio Shack, 5 $. I don't think there is any quality
difference.
Where you might run into problems is physically installing it into the wall
jack. If it is a newer flat wall plate with nothing else, it will fit. If
it is a wall plate with dual jacks (like a LAN beside it), it might overlap
the other connection and not fit. To solve this, try to put the splitter in
the back of the FAX machine but there might not be room there.
Also, old style wall jacks that have the jack hole sideways on the surface
mount box may present similar problems.
So to avoid these problems, you can buy a splitter patch cable. Same as the
one piece small splitter except it is a cable. Then you will not run into
any other problems.
And one last extremely rare problem is having too many devices on a phone
line. Each device has a ringer equivalence number on it and all devices on
a phone line should not add up to 100. I don't know the exact details of
it. In Canada, the phone is stamped with LNxx where xx is a number. My
phone is LN10, the kitchen phone is 10 also.
I don't remember all the details of how this works, perhaps someone in this
group has more knowledge or a link to a web site.
Other interesting things you can get for the phone line. Two phone numbers
on the same line, each with "distinctive" ring patterns. This allows the
FAX machine to pick up the line if it is the "FAX" ring you designated. The
FAX machine has to have this feature or you can buy a ringer box to do the
same thing. Modems have this feature too most of the time. You can also
get "Privacy" jacks, this somehow allows the device connected to it no to be
interrupted when someone picks up another line in the house. So it would
protect your FAX transmission from being messed up or if you have Internet
Dialup, not loosing your connection or if you don't want someone to
eavesdrop on your conversation by picking up another phone. I don't know
how well the last device really works. Just the blurb I read on such a
device in the store somewhere recently.