Do helium trucks get lighter when full?

It's an interesting question. First, if you want to be very precise, the truck will always have the same mass and therefore weight no matter what it's full of. If the gas was kept at atmospheric pressure in the truck, the helium would exert an upward force on the truck, so if you put the truck on a scale, it would "weigh less." But the helium in trucks and tanks are always compressed or kept at a higher pressure (so you can fit more). At the higher pressure, even helium weighs more than air at atmospheric pressure. So the truck would "weigh more" on a scale. This is why helium tanks don't float away.