That hose is in no way connected to any HVAC related noise IMO, so you likely have at least 2 separate issues.
Also, it is good practice to swap out the water pump with the timing belt. If that was not done, I'd be suspicious that other corners were cut too. And, it is a used complicated car with a lot of miles. So, you probably have more issues than that. IMO, this is a normal part of the purchase process and we've all been through it. Find them, fix them, and be happy.
Going back to your noise:
The A/C compressor is in that general area, and unless you manually turn it off, does often come on even when the heat is on. Turn on the fan/heat, and make sure the A/C compressor is OFF (not on auto). Does it make the noise then, or not?
The Hose:
You DO want to swap that hose, but I suspect you may want to do other cooling system things at the same time depending on the condition of them. Lower hose of the same age? Thermostat? Any browning on the radiator? Heater tees are almost a given. Water pump, if it is leaking or making noise. (this would be all the time the truck is running and proportional to engine speed)
Other stuff:
Fluid condition (oil, trans, xfer case, diffs, brake, AHC), filters (fuel air), plugs, belts/idlers/pulleys, ball joints/tie rods, sway bar/diff bushings, AHC globe condition/pressure-Tbar adjustment, etc etc etc.
Hopefully none of this is news to you.