It is posible, yes. It would be as simple as opening the pack and carefully extracting the cells to solder to your battery management solution. The issue is quality assurance and general safety, generally there's no way to know the quality and reliability of the cells before you use them. However if it's an OEM Asus battery, then the cells are likely of decent quality. Flat lipo cells need to be handled carefully, and properly thermally managed to prevent swelling and rupture. Cylindrical li-ion cells are safer, more durable, and don't require direct soldering to use.
There's also the factor of how to position the cells in your case. Li-ion cells are convenient in that their height actually makes room for tall-ish things like your fan and heatsink and also provides wire routing paths. If you want to use lipos, you'll have to figure out a safe place to put them that doesn't occlude airflow or risk getting poked by board components. This usually means that lipo builds end up being wider, while li-ion builds are a bit taller.