Yes, a single phone line can share both a fax machine (or computer running fax software) and a regular phone. A modem can be on the same line as well.
All on the same phone line with the same phone number
If one of the items is in use, the others will not work. For example, if the fax machine is sending a message, the phone line will ring as “busy” to anyone calling the line it is on. As well, if the phone on the same line is picked up (or the modem connects), the fax transmission will fail.
One challenge with this approach involves answering machines or voicemail. If the phone line starts ringing, either the fax can answer or the answering machine can answer, but not both. Some fax machines have an optional answering machine. However, these models are difficult to find.
All on the same phone line with different phone numbers
Some phone providers have the ability to connect two phone numbers to the same line. Each phone number will have a distinctive ring when called.
Some fax machines can detect the distinctive ring – it is a feature called DRPD (distinctive ring pattern detection). When activated, the fax machine will only answer the designated ring. This helps for having an answering machine and voicemail work on the phone line.
The most popular alternatives to putting a fax machine and phone on the same phone line are installing a second line or using an online fax service.
A second line ensures that there is no conflict between the fax line and the regular phone line. Typically it is close to the same cost as the original phone line, as well there are likely to be installation costs to wire the second line.
An online fax service manages the phone lines as well as the software and behind faxing.