Maybe a little if you also do the entire exhaust system. The headers are just one part of a long tube going from the air filter to the tail pipe. So better extraction of exhaust means little if it gets bottled up in the mufflers.
Often the small gain in fuel economy is overset or even negated entirely by the driver pushing the car a bit harder because he likes the sounds it makes.
If you are asking "will headers pay for themselves in gas saving", I'd say that's going to take a long time. Let's say you gain 1 mpg. Calculate that out in gas savings over the cost of headers + new exhaust. 15 mpg vs. 16 mpg over a year? That's save you about $100. 2 mpg = $200 per year.
Also header bolts often loosen up and need to be periodically tightened, or you should at least get special lockers for the header bolts. And you have to buy good quality or they'll leak.