Schools start accepting applications as early as June 1st and Organic makes up about half of the chemisrty section of the DAT.
I am a junior in undergrad right now and I was in the same position last year. I also wanted to apply for early admission. The dentist I worked for strongly encouraged it. My advisor did not. I finally decided NOT to apply for early admissions for the following reasons: it was August and I had not taken the DAT yet (you can still apply if you take the DAT in Aug, Sept, or Oct but if I didnt do as well as I would have liked to, I wouldn't have enough time to retake them) and I want to go to school out of state, which is more difficult to get accepted w/o a BS.
My advice to you is this: look into the schools you wish to apply to and check the stats of the classes they admit. How many do not have a BS? If you take organic over the summer, make sure you get a good grasp of it b/c summer classes go at a much faster pace and O. Chem is an important part of the DATs. Also, check if you current school has a 3-4 program with any dental schools. My school has a 3-4 program with Temple, which almost guarantees you admission as long as you have 90 credits, the required science classes, and have a decent GPA and DATs.
The advice of the dentist was to go for it. It's one less year of undergrad tuition, you get right into doing what you are interested in, and you start making money one year sooner.
So if you can do it, go for it!!! Just remember, you will need a strong GPA, DATs and recommendations b/c most other applicants will have an edge over you b/c they have a degree.
Good luck in whatever you choose to do!!