Can you shut off the cold water intake to hot water tank to stop a leak not in hot water tank?
Yes, but there still is all the water stored in the tank plus the water stored in the existing hot water lines throughout your home that will eventually leak out.
If you intend to install a hot water heater (HWH) yourself and you do not have valves to isolate the existing plumbing then turn off your main water supply, drain the water from your home using the lowest level sink, then attach a hose to the bottom of the HWH and drain the tank. When you install the new HWH install new shutoff valves. (Hint: Check with your local city plumbing and see if an expansion tank is required.)