Yes. I think it is possible. Here's my situation. In jan i took the SAT but had to cancel due to a proctor timing problem that messed me up. I had a whole lot of crap in Feb and took it with very little studying in between in March. I got a 2130.
I didn't do anything since then. No SAT whatsoever. I studied for AP testing and SAT2s. Thats it.
Three weeks ago, I took a test. I got a 2280. Remember, no studying whatsoever in between.
Two weeks ago, after going over maybe 100 direct hits words, I took a second test. 2350.
Today, I took a test with about 150 words memorized. I didn't really feel up to it and didnt finish some sections. I got a 2250 with my lowest math score since like november *****. Btw, I accidentally had my AC on full blast. I was shivering when taking it lool
Honestly in my case I really feel I am capable of 2350+. Making a claim that you want a 2400 is kind of audacious. Its very difficult and a lot haa to do with luck. From my experience, I say its fully possible to go to a 2350+ in 12 weeks. Just study carefully and efficiently. Although I didn't study persay, I guess I subliminally worked on my comprehension skills while doing all of that studying.
Good luck. And remember, 2130-2350+ (possibly 2400) is fully possible.