I recently took the SAT without any prep, and I got an 1100. My target score is a 1400, but I don't have much time to devote to studying right now. Could one month of intensive studying leading up to my second attempt be enough to raise my score by 300 points?
One month probably won't be enough time to raise your score by 300 points. Typically, an improvement of this magnitude will take 150 study hours or more. If school is in session the month before you take the test, there's pretty much no way you'll have enough time (30 hours a week is almost a full-time job!).
Of course, not everyone will need exactly 150 hours of studying to improve by 300 points. This is a ballpark number, especially because we don't yet have much data on how easy or difficult it is to improve scores on the new version of the SAT. It's possible that you could improve by 300 points in less than 150 hours since you haven't done any prep in the past. Students who are less familiar with the test tend to improve more rapidly as they get comfortable with the format.
Still, I'd recommend spreading out your studying over the course of at least three months if you want a solid chance of reaching your goal. This will give you time to thoroughly analyze your weaknesses on the test and practice under less stress and time pressure.