For the elastomers, there is a short break-in period that might last for maybe 2-3 rides (or 1 really long ride) but it is pretty subtle. You would not expect the "feel" to really change that much after break-in - most people don't even notice it but sometimes if someone has a setup that feels just too stiff the break-in makes it feel just right.
So, given that, there are a few things to think about. The first is that you probably won't feel the stem moving much at all under normal riding conditions - you should feel it if you hit a bump or a something like that but normally it will be moving a good bit but you won't actually feel or perceive that. One of the nice things about the stem is that it is pretty transparent - and after you ride with it for a bit you will likely forget it is there totally - but if you jumped on a bike with a rigid stem you would suddenly feel a big difference.
With a flat handlebar, you are limited a little with how much force actually goes into the stem which means you might want to try a softer elastomer first to see how that feels. It is always good to experiment a bit with the elastomers to find your perfect fit.