That's right. It's not an electrical interaction issue. My Artemis phono stage has a single input, so only one arm was connected to the outside world at a time. The other arm was just sitting there.
Now I don't know how much can be generalized from my experience. For instance, if you're using a table with a wood base like the Teres, would the presence of an additional wood mounting platform make any difference? I don't know. But I suspect adding a second arm on a wood platform attached to another all-metal table would have a noticeable effect on the sound.
The only way to find out is to try it.
Dave