I've done APRS just as you described for a number of years. Scanner's audio output to the PC's sound card running a TNC program, which then sent the data to the APRS program running on the PC. That 'TNC sound card' software OR a separate TNC is required unless the APRS program has a TNC written into it. I'm not aware of any such APRS program that includes a TNC.
There are two basic ways of operating APRS they deal with how the data is received, RF or via the internet. One method requires a scanner/receiver to supply the RF that is then converted to a form the APRS program can use. The other method is by receiving the data from the internet which requires an internet connection instead of a scanner/receiver to receiver that data. The information from the internet is usually already in a format the APRS program can use. As long as the program receives the required data, it doesn't really matter where that data comes from, the two sources, RF and internet, can be combined if you want.
Have fun.
- 'Doc