I thought that there was (i.e. that the counterpart to Worf's console on the Hathaway had just been removed or dismantled, leaving his as the only one left) but that's not the case. On that ship, the captain's chair and that one console are all that there is at that location. You can tell by the pedestal they're sitting on. There's no room for an equivalent console on the other side of the captain - the pedestal is built for exactly that width, for the command chair and the one console. That's it. Neither of them is at center.
Well, by "other side of the bridge", I meant that there might be a match to the other console that we see on the side of the bridge when everyone first comes in. We don't see the corresponding part of the set on the starboard side, so there conceivably could be one sitting there. In production reality theyre probably wasn't, since that and Worf's console are two elements of a pair of consoles we usually see on guest starships; but in-universe, assuming the side console was part of a symmetrical setup, there could have been a third console on teh starboard side of the bridge.
But as I mentioned earlier, I like the notion that the two-seat central config we saw was hastily slapped together by someone before the Hathaway was towed to the site of the exercises. IMO it could easily represent the bare minimum that a crew would need to fly and fight the ship (something we sorta see again in "Relics" with Geordi manning the CO seat with con/ops panels and Scotty backing him up on the engineering console in that case) so that's what they started with.
For all we know, in the latter part of the episode both the side console we see and a potential third console were both manned and simply out of sight since we don't see them at all after the establishing shot later on. IMO no, but we can't positively rule it out.