Couple things to consider.
1. If you use company money to pay for your MBA and leave early, you'll just have to reimburse the company for what ever the tuition costs are. This is what I did. Actually, my company had a 2 year vesting period, but since it was a part time MBA that takes about 3 years, my first year of tuition was already vested, so I just had to pay the balance of two years. In my opinion, I don't see any difference between doing it yourself and using company money; company money would essentially be an interest free loan. Additionally, your company cannot force you to stay and work; you'll just have to pay them back what ever you owe.
2. If you decide to get your MBA without help from the company, it may raise questions that your looking for an exit. I'd assume your manager would know your getting your MBA.