Sorry, but don't run it without coolant.
For starters it will overheat in certain areas of the motor (cylinder head) quite quickly.
Also, the water pump may get damaged running with nothing to push against.
If the new gasket is properly seated then it won't leak.
What I do is I stick the gasket to the valve cover using Blue Hylomar.
That way when ya take the cover off to adjust the valves the gasket stays on the cover.
When ya put it back in, if yer careful, you can make sure that the gasket is located correctly.
Once ya have the rad, etc back on you can still see the gasket if ya use a flashlight from the sides.
While yer in there check all the crush washers on that Y tube and if it's rusted, take it off and Rust Remedy & paint it before ya refit it.