Yes they were deployed. I tested both as German as well as American to check how many soldiers were cowering.
I'm sure shorter range is better but that goes both ways and, in my admittedly limited experience with quick battles, HMG's seems generally to be overwhelmed very quickly at shorter ranges, as if they simply can not deal out enough firepower against multiple targets.
But it is my understanding that HMG's could easily be deployed several hundred meters away from front positions and expected to support them. I just don't see how that is gonna give any good effect in this game if they can't deliver more firepower?