Not only. Depends if TV is master or slaved, and audio routing.
I recorded a DN2 squarish sine wave in TV, played same note on DN2 (left) and TV (right) with midi sync, and mesured timing difference by recording them.
Recording with Octatrack, DN2 left, TV right :
DN2 master : TV is 9 ms late
TV master : TV is 3 ms AHEAD !
These results would be the same with a mixer.
So TV master is no brainer thru a mixer…if DN2 isn’t plugged into TV.
DN2 audio plugged into TV :
DN2 master : TV is 4 ms ahead !
TV master : TV is 15 ms ahead !
So with DN2 audio in TV, seems better to have DN2 master…
TV audio plugged in DN2 :
TV master: TV 2 ms ahead
DN2 master : TV 9.8 ms late
TV master, DN2 comparison between a note played in DN2 (left) and passed thru TV : 11.4 ms.
The latency between what comes in TV inputs and its ouputs seems to be constant, 11.4 ms
(Results may also depends on how fast DN2 and TV plays their notes, how I edited the square note, maybe truncated attack ?)
Recorded with Octatrack, here is TV master (DN2 left, TV right and ahead !)
I mesured 12.5 ms between DN2 and DN2 thru TV input, same note played from TV. I wouldn’t say instantly.