You can, though you probably don’t want to. It’s not that fresh ginger is more pungent, it’s not. The reason: because fresh ginger contains more gingerol compounds, which, even though they are closely related to the capsaicin found in chillis and the pepperine found in pepper, are what are responsible for fresh ginger’s bright, enlivening flavor. Its only when ginger is dried that those gingerols are transformed into compounds known as shogaols, which are twice as pungent, and give gingerbreads and gingersnaps their characteristic bite. Heat mitigates some of this power, transforming shogaols into zingerones, which are still more aromatic and sweet. And in case you’re wondering, no, I’m not making these words up.
Fresh ginger, though it does give gingerbread a kind of refreshing tingly tang, doesn’t provide the same experience as the dried stuff. However a nice alternative if you’re looking do do something a little different with your gingerbread this year, is to used candied ginger which brings a bit more complexity to the mix. The only issue there, because candied ginger is so much milder than dried, is that you’ll need to use rather a lot of it. A general rule of thumb is a full half cup for every tablespoon of dried ginger your recipe calls for. Simply measure it out in chunks, pulverize it to powder in the food processor, and you’re ready to go.
All of which is not to say there’s anything wrong with dried gingers, though not all are created equal. Should you wish to up the ante there quality-wise do your best to locate some Jamaican product, which as a rule has a more delicate and sweeter flavor than Chinese or African, which are much more pungent and powerful. Australian or Indian ginger, being almost lemony, are also good choices.