I was about to quote the TNG Companion or some other book which mentioned that the producers basically had everyone go to Engineering because the Battle Bridge set had already been torn up and put back in storage. I then remembered that "Brothers" and/or "Family" was actually filmed before BOBW II, so the BB set may not even have been built yet. *Then* I remembered that studio space, being always at a premium, may have also prevented them from mounting the Battle Bridge set anyway since they would have had to use the space for Soong's home and the jungle outside.
I do like the notion that Engineering would have been a better place to troubleshoot environmental and navigation problems, if the Main Bridge may have been seriously compromised. Perhaps in a similar circumstance where the Main Bridge would become uninhabitable for non-combat situations, everyone would go to engineering first with one person on a given bridge shift designated to go to the BB to fire it up and/or check systems from there. Thus, when Data headed to that turbolift Picard gave a curt nod and kept going, especially since no one was going with the Android (everyone else left via the other two lifts, with more than one person per lift).
I guess there'd be nothing preventing people from leaving via the supposed ramps down to deck two either, but it's not like anyone was in a big rush. OTOH, when the nanites had smogged up the Bridge in the previous year, it took only seconds for the (same?) reverse pumps to remove the noxious fumes...