I have done it & it works, normally I multiply by making 3x3 doors with single block over each, on top of any villager house, they cant get to the doors above but will continue to breed, there is a limit to villagers per door as well its something like 3-4 doors to spawn/breed a villager, plus I dont go checking out most of these tubers I work out most of my own game issues, for me thats the fun of it, I check the mods wiki & work out the rest from there, in this case it was vanilla MC so..No, not just a door with a block above it.
A door with more blocks above it on one side of it than the other, as to constitute a roof compared to a porch, or even open sky.
I recommend checking out some DocM77 vids on Villagers and iron golems etc.
Unlike most of the rest of stuff which people recommend that's hidden somewhere amidst 70 episodes of a LP, such as Etho or Direwolf20, this is a dedicated tutorial.
on one server I built a villager tower block, it spawned way to many I had to drop it to 3 lvls high & even that spawned a lot of villagers & golums, was a mindcrack 1.3 server if I remember but not a lot has changed in villager spawn mechanics.
I still make then now & then, its a must have if your playing a sky block map, trap 2 infected villagers & use potions/apple.