It could happen, but the circumstances to do it wouldn't come about in the normal couarse of the game. Then you will need a half-hour or more of constant banging on it, racking up enough hits to do some real damage. Flying of ships will be limited to fighter craft. For single player, the Starfury and Thunderbolt. Multiplayer will have ships from many races, including the Minbari Nial, the Centauri Sentri, the Narn Frazi and the Drazi Sky Serpent fighters.
Cockpits are different for every vessel.
Each have their own distinct console and HUD configurations, although there are commonalities. Things such as targeting and radar are more or less uniform. Seen in the fifth season, there has been no confirmation to its appearance. The most popular of B5 ships will be flyable if we do good enough in the campaign. No idea for multiplayer.