Beta backer here, have already wasted a ton of time in this game. "Fly-by-wire" is called "flight assist" in the game, and it works essentially the way you describe.

You mostly get the sort of gravity effects you're describing in the fast-traveling "supercruise" mode, where the proximity of a large mass severely slows you down. The effect is handy for slowing to approach speed close to stations, since they're generally close to a planet or a moon.