I haven't seen any data regarding that but the manufacture's specify the length for a reason so I would assume it is important. If the meter is too close to a fitting it could read higher or lower. Close to fittings, the pressure varies considerably in different locations of the pipe. I think the specification are set to ensure that there are no local eddies or pressure differentials. Any closer and there is no guarantee.

Venturi type flow meters are not all that accurate to begin with. They usually have an error which is 10% of the maximum reading so if your flow meter goes up to 100 GPM, that is +- 10 GPM. Unless you spend a lot of money for a paddle wheel flow meter, the accuracy is probably worse than a direct head measurement.