Here's a chart showing natural gas flow through different pipe diameters. You can see that in a 10 foot length of pipe 2" in dia. decreases from 4020 cf/hr down to 678 cf/hr in a 1" dia. pipe.:
I understand the difference between the pipe cross section affecting flow, but your original assertion is saying that going from a smaller pipe to a larger one will somehow reduce the flow rate. This chart doesn't say, going from a smaller one to a larger one does anything. if anything, this chart supports the opposite.