Yes, the TZT3 and GP1971F can be on the same NMEA 2000 bus. The GP1971F could share any good GPS data, transducer depth, water temp etc. If the transducer is on the TZT3, then it could send that depth/temp over to the GP1971F. While the GP1971F is not a Navnet, it will share basic NMEA 2000 data. You will not be able to use any TZT3 radar or sounder pictures on the GP1871F or see the GP1871F sounder on the TZT3. The GP1971F is not an Ethernet device like another Navnet display.
If we look at the combined output lists of either device. Some of it is dynamic (e.g. 129025/26) and some of it intermittent (129283/84).
I recommend If you have a specific data set you're interested in sharing, print out these pages of the brochures and compare the inputs and outputs of the NMEA2000.