In general, no. For almost all words, the definition is inferred by lexicographers from examples of how it is used in real life, and typically is not precise anyway. Also, if you ask someone for a definition of a word they know well, they will generally try to construct one on the spot, and often it won't cover all the uses that they themseves would recognize upon consideration. Usage is king, and definitions are secondary. This is a point that Wittgenstein is famous for, but lexicographers already knew it, I think.
However, for some technical terminology, a very specific definition has been constructed. For those terms, using them at all may suggest you are familiar with the technical definition, and so perhaps you can't really use them correctly if you don't know the definition. But, even then, it might fine if you just know enough to be sure you are pointing at the right class of objects.
Added later: I'm going to make this answer a little woolier by talking about the specific example. In the specific case of trying to show that all Xs are Ys, you often do need to establish definitions for X and Y. If you are even having to have that discussion, there probably isn't an agreed-upon definition for each, so you have to give the definitions you want to use. Are embryos organisms? Well, it depends on what you mean by "organism".
In some cases, though, it's easier to know that all Xs are Ys than it is to come up with a definition for either. I can tell you for sure that all chairs are furniture, but don't ask me to give you a precise definition for either category.