Long ago, in the Before Times, when cars didn't have heater shutoff valves we would put one inline - just a simple brass ball valve.

You want this, otherwise there will always be airflow across the heater core that will get heated up.

IME, just having the coolant flowing in a heater core leaches a pretty good amount of heat into the cabin. I have shutoffs on my tractors and heavy trucks for summer use to completely close the flow off to the heater or I'll sweat my ass off.

It should be fine in terms of not damaging anything. The only downside is that it will heat the cabin somewhat until you replace it.