Good question. It depends on the airline, (SWA for example requires the 737) and whether you have experience in the airplane. Most airlines, I think, will place more emphasis on a type rating if you have flight time in the aircraft, versus going to a school just to get the type.

Personally, I have ten type ratings listed on my ATP. Did I get hired because I was typed in one of the fleet types at my employer? I don't know, but I'm sure it did not hurt.