I wish there were ground versions of DSEs so that you could 1) test these things out easily, 2) have known enemies in repeating missions - unlike the explore hit-and-miss, and 3) have a place to test my ground builds before I go into the STFs.
I've looked through Foundry missions for something that would suffice, but haven't found anything satisfactory.
I just put my entire Jem Hadar set on one of my bridge officers and I noticed two things. First, the passive abilities lit up one at a time as I equipped the armor. Then I saw the officer use shroud during my first ground battle.
So I'd say yes the bridge officers do utilize the bonus abilities.