All the recipes I have seen for a Galantine just cooks the prepared chicken in an oven pan. What would you generally expect from the Galantine if it was cooked in chicken or vegetable stock?
Although many recipes call for roasting, poaching is actually the traditional way to make it. Cooking it gently helps keep it juicy, and cooks the filling without over-cooking the delicate chicken breast.
Many recipes call for it to be tightly wrapped in plastic wrap, kind of an improvised sous vide. That prevents the filling from leaking out into the water, and keeps the galantine from falling apart. If you want to imbue it with flavorful poaching liquid, you might want to wrap it in cheesecloth, to ensure structural integrity.
A couple of example recipes from teh intarwebz:
There are a couple of ways to cook and serve a galantine or ballotine...roasted on a rack or wrapped in plastic wrap or cloth and poached...so it depends on your recipe. Whether you serve it hot or cold may also be a factor. For a hot preparation you will want a crisp skin. So, you will need to consider that. However, to answer your question directly, using stock instead of water, in any recipe, will generally impart more flavor. Of course, if you are cooking something wrapped in plastic, it would not matter.