Yes, you've got all the plumbing to draw from a jug of vinegar and pump it into the WH. Close the valve from the water tank, open the valve on the flex hose, and suck away. I'd finish with a jug of water (or open the tank valve) and draw a bit of water into the pump and line.
Once the vinegar as had a chance to loosen all deposits, be sure to flush the tank with a spray wand
to prevent crud from blocking aerators.