Simon Brown (G4ELI) excellent SDR software SDR-Console v3 has a very good satellite tracking integration. In version 3 it is also possible to control an external radio via CAT. This is explained in detail here.
This means that it is possible to control the transmitting radio for doppler at the same time the SDR unit (receiver) is following the downlink also with doppler. Very nice!
I have made some tests with my Yeasu FT-817ND and most of the times it works very good. Sometimes the connection between SDR-Console and the radio is lost, but this is fixed by restarting the “External radio” in SDR Console. Below is a short video of my test.