Hasn't been done before, and I haven't seen real life departments move trucks unless they need to make room for other responding companies. Would be interesting to see if it's doable, though I have a feeling it's not or it already would have been done.
It's called forward lay of the line, it's used mostly where a hydrant isnt exactly near the hydrant, so instead a firefighter hops off at the hydrant, ties around it, then the engine proceeds to the fire with the hose reeling out of the bed of the truck as it goes. Saves lugging the hose yourself to the supply line if it's a decent hike away. It isnt the most common practiced method of deploying the hose, but it's very effective in areas where the hydrants are few and far between and there is no other alternative for sources.
allso a 2nd truck hooks up to the hydrant and ramps up the speed at which the water is fed to the truck further up the road