You didn't say your replacing any fluid, so if it is low on fluid then; yes not putting antifreeze in will cause it to over heat.
You may have other issues, if it continually is getting low on fluid. Reg water will eventually rust parts and may clog your system, you will need to do some serious flushing to clear it. Get ready for hours of flushing repeatedly. ALSO; it can and will rust out Freeze plugs on your enging block, causing water to leak out. Anti Freeze should be mixed 50/50 with water. You can buy it already premixed, or concentrated and it tells you right on the jug how to mix it. 1 more thing could be a problem, check all your hoses to make sure they are not leaking or kinked any where.
Running an automobile without water can cause serious damage which could be very expensive!
Don't do it.