Yes, it’s very possible to use an 18v battery in a 14.4v DeWalt drill. It is not important which voltage of battery you are using, what counts is the Ampere- hour.
There are more than 12volt batteries with 18 amp-hours of energy. You can use these batteries for your DeWalt 14.4v drill. For safety purposes always check the voltage rating of both batteries before starting to use them together. But there are several considerations to think about.
DeWalt 18v batteries are designed to be used only with DeWalt tools. Even if the voltage rating is the same some differences like Ah might affect your Dewalt drill speed performance. Because you would be getting more energy from the battery which would make the tool work harder and wear out sooner. So always check before you buy any new batteries for your Dewalt 14,4v drill that they are manufactured by DeWalt or at least compatible with it. You can use Dewalt 12v battery in Dewalt 14,4 v drill as well because these two voltages are safe enough to use together without damaging anything inside of your charger or tool. Simply put first on first place, second on second place, etc.