Can I connect my laptop that runs on 18.5V directly to a 12V battery?
There is no way to know from the outside how the laptop will react to 12 v, but probably not well.  It may also not react well to having the battery completely removed.  It could possibly be integral to the internal regulation.

The safe thing to do is to get a "car charger" for your laptop.  These are intended to work from 12 V car power and supply whatever power your laptop needs.