It depends on the topology of the amp. Some do, some don't.
There are 2 ways triodes are used in audio circuits. As a voltage amplifier in what is called common cathode configuration which does invert polarity and has relatively high output impedance. The other way is as a current amplifier (or buffer) in a cathode follower configuration which has no voltage gain but low output impedance.
A very common topology is to have a Common cathode stage followed by a cathode follower so you get voltage gain from the first stage and then low output impedance from the second. You can then build a preamp with only 2 tubes.
If you add another voltage stage after the first you get a second inversion which puts it back to not inverted. And so on.
There are 2 ways triodes are used in audio circuits. As a voltage amplifier in what is called common cathode configuration which does invert polarity and has relatively high output impedance. The other way is as a current amplifier (or buffer) in a cathode follower configuration which has no voltage gain but low output impedance.
A very common topology is to have a Common cathode stage followed by a cathode follower so you get voltage gain from the first stage and then low output impedance from the second. You can then build a preamp with only 2 tubes.
If you add another voltage stage after the first you get a second inversion which puts it back to not inverted. And so on.