That's a vacuum hose and it powers the fuel pump. It's called a "pulse pump" because it is powered by pulses of vacuum from the engine that turn/power the pump. If you don't have the vacuum line connected to the pump, the only thing moving fuel from your tank to the bowl in your carburetor is gravity, and if the carburetor is at or above the level of the fuel tank you're likely getting little to no flow. I believe the vacuum hose is 1/8in or 3mm ID. You can use fuel hose if it's the same ID, but on some GC/GCV engines the nipple on the engine is at a right angle to the nipple on the pump, and you may have difficulty bending the stiffer fuel line to fit.
