Structurally and tonally no drawbacks. It will certainly add a few levels of difficulty particularly for a first build.
Wait a minute....I'm assuming that when you say all from one piece of lumber, you mean making the neck and body all from one piece. If so, then details like fretting, headstock shaping and drilling, routing and so on are trickier, especially for a first build, because you have a whole guitar hanging onto the other end of the part you are working on. It can be done and done well. See one posted by Pauliemc for the most recent example here.
If youare talking about just making the body from one piece instead of a glue up then there are no other drawbacks at all, and you've saved yourself the step of the glue up. You are just going to spend more money and waste more wood as was mentioned.
SR