Organic matter will surely decompose faster than mineral matter. Not only that bigger pieces will become smaller pieces, but the chemistry (chemical composition) will change too.
About the 100%, that is ambiguous. If you mean "what will happen in a few thousands of years", then 100% decomposition is highly possible. In the course of a few years, 100% is quite impossible.
So can I use the compost ... and not run into the issue that the compost decompose over time and the grass will sink?
Sinking is very likely. Compost is a quite fluffy matter. Even if you compact it, it will still be spongy. In time, the sponginess will go away, and the sinking will be obvious.
Sinking will have 2 big reasons:
- Water (from rain, snow, irrigation) will force the air inside the compost to go up. When the water will evaporate, it will force the compost to become more compact (while absorbing a smaller amount of air than was released).
- The grass (or whatever you plant there) will consume the compost, and this the actual volume of the compost will decrease, even if a little.
As @Stephie mentioned previously, the "pure" compost has a high chance to actually chemically burn any living plant you might want grown there.