The fuel pumps that are internal to the forward and rear internal fuel tanks just push fuel from the internal tanks to the engines (and APU). Each external tank will have its own individual pump that pushes fuel from the external tank to one of the internal tanks. If you turn off your forward and rear boost pumps, but leave the external tank pumps on, you will still get fuel from the external tanks into the internal tanks.
There are two reasons (well, three I suppose) to have boost pumps pushing fuel (I'm now talking about the boost piumps inside the forward and rear internal tanks): First, during engine start, the engine-driven pumps need help. Since they're barely turning, they don't provide enough fuel pressure for the engines to run. Second, at higher altitudes, the suction effect of the engine-driven fuel pumps can cause fuel to cavitate, resulting in air bubbles in the fuel. Air bubbles are very bad for the engine-driven fuel pump, very bad for the fuel control on the engine, and obviously very bad for keeping the fire lit inside the engines, possibly resulting in a flameout. Third, your engine-driven pump could fail (in theory, anyway).