As you heat the water, if no taps are open and there are no leaks, the initial expansion balloons any flexible pipes (like say those to your washing machine if you leave the valves open, and any faucet or toilet supply), then when they reach their limit, you're trying to balloon metal, and the pressure will quickly spike from there. Without a check valve, that expansion just pushes back out into the supply where there will be some capacity to absorb it. The total volume of expansion depends on the temperature the water starts at and how much water is being heated, and the delta in temperature. Without using hot water, raising the aquastat on the WH slightly to cause it to come on, the delta isn't much, therefore, the increased volume will be small. From cold to normal WH temps, in say a 40g tank, you might see a couple of cups. In a closed system, that's easily enough to reach over 150psi, where the WH T&P safety valve can open to relieve it. WHere I live, in a cold snap, mu delta-T exceeds 100-degrees (incoming is very close to freezing, and my tank is set to 140-degrees).
To properly size an ET, you need your worst case incoming water temperature, the size of the WH, and what you've got the WH set to produce that generates the delta T. The calculators on the ET manufacturer's website will then tell you the size tank you need. Do not go smaller, but larger doesn't hurt (except the bigger ones cost a little more).
Your PVC irrigation piping doesn't like those pressure spikes, either, so you would want to protect them with a hammer arrestor. The strength of some pvc piping degrades if it is exposed to UV light, so it is more susceptible to fracturing, so helping to relieve stresses from water hammer are prudent. Generally, you want that as close to the offending valve as possible for optimum results. An ET for your WH will be further away, but still would help.
In some places, when an irrigation system is connected, they not only want a special check valve, but annual certification from a licensed inspector to verify that it is working properly. Having that protects not only your house, but the entire community near you. A simple check valve certainly helps, but isn't as good as one designed for irrigation.
So, I'd install an ET, see what that does for you on spikes, and then seriously consider adding a hammer arrestor on the supply side to your irrigation control valve(s). WHen you stop the flow rapidly, it's like the water hitting a brick wall and it bounces back from that. With a hammer arrestor, it compresses some air in a chamber. You want an engineered one, not a home-made one that's just a air column, as the air in one will be absorbed after a few months.
Don't know what part of IN you are in, but with the water supply coming above ground before going into the house wouldn't be allowed around where I live...it would freeze overnight. When the water is moving, that isn't likely to happen, but overnight, or say when nobody is home during the day, that water is just sitting there, and the exposed piping would just freeze and split around here.