In Catan, should development cards be drawn one at a time?
Buying multiple Development Cards at once is a legal play.
The rules state this:

Build
Now you can build. Through building, you can increase your victory points, expand your road network, improve your resource production, and/or buy useful development cards. To build, you must pay specific combinations of resource cards (see the Building Costs Card). Take the appropriate number of roads, settlements, and/or cities from your supply and place them on the game board. Keep development cards hidden in your hand.

(Taken from this answer: In Settlers of Catan, are all actions on the same turn simultaneous?)
So, spending resources can be done in bulk, with no distinction between roads, villages/cities or development cards.
The Rules Almanac, an appendix to the main rules book, has some clarifications and additional limitations to playing Development Cards. These are that you cannot play development cards on the turn you buy them, and can only play one development card per turn. VP cards are an exception to both of these rules however, as you don't play them but reveal them when you get to 10VP.
Although the almanac states that buying your tenth VP ends the game, it also allows for buying in bulk.

The FAQ doesn't exactly clear things up either:

Victory Conditions
May I continue scoring points after having reached the number of victory points required for a win?
Answer
This could make sense in a private tournament where the scores from several games are added up. For individual games and official tournaments, the following applies: You have won as soon as you have reached the required number of victory points on your turn – and then the game is over.