To answer your question directly, it is OKAY to run the engine hard mounted on a test stand. It does NOT NEED to have a shock absorbing mount.

Often there is more than one way to accomplish something and either mounting the engine in the model and fly it or do a test stand run is a matter of personal preference. Since you are new to gas engines I would suggest to run the engine on a test stand. That way you can learn a bit about the starting process and initial adjustment of the high and low needles without the danger of risking the model if something goes wrong.

The engine doesn't know if it's on a test stand or in a model. If the engine is mounted in the plane and flown, it will run a little higher rpm (once airborne) because it will unload a bit. It will also get more cooling air since it is flying through the air in addition to whatever air the prop throws back onto the engine. On the down side, and assuming the engine is in a cowled plane, you may encounter overheating if you haven't allowed for adequate ventilation to get the hot air out of the engine compartment. An overheat condition will almost always result in a engine that stops running. Now you risk the plane if you can't glide to a safe place to land.

Therefore, I suggest you test stand run the engine for a number of reasons. You can always take an electric fan and direct the air flow at the engine which will give you additional cooling beyond what is given by the prop. That would be similar to the same effect that occurs if actually airborne. It gives you the opportunity to become familiar with running the engine without risking the plane. Learn how to tune the engine (setting the needles) without risking your plane. The engine should run with the needles set at the initial factory setting but is almost never the optimum setting for a engine and you need to learn how to do that. Also as the engine breaks in, additional adjustment to the needles will probably be needed. So, for the first gallon or two of gas, expect to have to make a few adjustments along the way. You certainly don't need to run an engine through a gallon of gas on a test stand but long enough to see that it runs pretty reliable.

By the way, you don't actually have to have a test stand. You can go ahead and mount it in the plane and do your test runs there without actually flying the plane. I don't do that because I have a test stand and I don't like to put needless vibrations to the airframe. These gas engines do shake a bit more than glow engines. If you do use your airplane as a test stand be sure to attach the wings as they help absorb the vibrations of the engine.

So, either way works. Again, its a matter of personal preference.

Indiomike