Hi! It is possible to get from 600 to 720 in that general timeframe and with that general schedule, yes. Of course, not everyone does.
Depends on many factors, including how effectively you're studying, not just how much. But if this is what you're really asking: Yes, this is generally a reasonable goal to set.
One note: I generally recommend that people plan to take at least 3 weeks post-course for review before taking the real thing. You'll have 1 week of homework after class 9, plus you'll want at least 2 weeks for general review (like studying for finals).
The homework we give you—if you did it ALL, including the optional / additional stuff—would take like 20+ hours a week. So you probably won't find that you have time to do more that isn't there. The real question is how you should prioritize everything that we give you because I wouldn't want you to do it all...the GMAT would be coming out of your ears.
Have you taken your first practice test yet? The data from that will help you to prioritize. You can also ask your teacher to advise you (I ask my students to tell me what they think based on their first practice test, to get them used to analyzing and planning, and then I tell them what I think).
If you think you'd want more support than that, we do also have an add-on product called Coaching—it costs money, but it's steeply discounted (Note: you have to buy it before session...2 or 3, I forget). Please do not feel that you need to spend more money, but here are the details just in case you think you'd like this. Coaching = three one-hour one-on-one meetings throughout the program with your instructor (or another instructor, if your schedule doesn't match your instructors)—to prioritize, to target weaknesses, to help you over stumbling blocks...basically to do whatever you need to make sure you're maximizing your study time as you go through the program. If that sounds at all of interest, talk to our student services team (800.576.GMAT).