Well certainly it is "possible." Is it probable? I have no idea.
Step one, make sure they will accept your late GMAT score. You will get an unofficial score after taking the test, but your official score could take up to 20 days to be reported to your school. (although during the slower season, you should be able to see it in under a week)
Your MBA admissions department will be cery familiar with these timelines, and will be best suited to give you advice. Don't delay, ask them first thing tomorrow. Because if they say they won't accept late official scores or your unofficial score (which, btw doesn't change, you are only waiting for your AWA to get scored) you are S.O.L. and don't even bother with the rest of this reply.
If they say yes, that this is fine, then start your work. Keep in mind you are working with a very compressed timeline here.
1. spend time familiarizing yourself with the format and types of questions on the GMAT. Get to learn the principles and especially the types of questions asked. You don't have very much time for this, so focus on th data sufficiency questions and the Critical reasoning questions. Sentence correction probably wouldn't hurt either.
2. Download the GMAT Prep tests from MBA.com. Take the entire test in one sitting including the AWA section. You need to feel (or remind yourself) what it is like to sit for 4 hrs for a high pressure test. After taking the test -
3. Analyze your answers. Both correct and incorrect. These will give you an idea of your strengths and weaknesses.
4. At some time during all of this, you should schedule your test. It would really suck if you did all this and find out all the appointments are full.
5. Practice, practice, practice.
6. If you are able, take the second practice test two days prior to the test. Again, the whole thing.
7. Usually people take the day off prior to the test, but for you, you might want to do more error identification and a few brush up lessons.
Good luck!