I'm still using arrays, so I might be coming at a slightly different angle to you, although I reckon it can be done more or less the same way with sprites.
So, once you've spawned your doors, you somehow pick two doors to link together. Set the walls of your rooms to solids, spawn a sprite with pathfinding (diagonals off) at the first door and plot a path to the second, using a pseudo-movement for the sprite (stepping one tile at a time, but every tick so it's as fast as possible) to go from node to node in order, leaving behind a trail of corridors as it goes.
Alternatively, you could use the stretch function to draw lines from one node to the next, then generate corridors on every tile where there's a line (come to think of it, that's probably a much quicker way to do it...) Repeating this for a bunch of doors should give you a nice network of corridors with lots of branching paths.
If anyone would like to help a brother out, there's a .capx below showing what I've been working on tonight. As you can see, I'm auto-generating rooms of random length and width just using a single map array, but I can't figure out a way to stop them overlapping. I tried making a function to test if the cells at Map.PositionX and Y + Roomsize X and Y were anything other than zero, but that didn't seem to work - I'm quite new to arrays though so I probably got something wrong.
Ideally, I'd like each room to be spaced at least one tile apart (walls included) so they can always be connected by corridors - if anyone can tell me how to do this, I'd be really grateful!
dl.dropboxusercontent.com/u/106247621/ProcGenDungeon.capx