No. The B-1 visa allows you to conduct business in the US, such as attending work-related conferences, meeting and events, but prevents you from receiving payment or working for an American company. You are not allowed to study using a B-2 visa or an ESTA, either. If the purpose of your trip is to enroll in a school or take a class, you should apply for a student visa (F, M or J). Doing so under a B-1 or B-2 visa is considered a violation of status and may jeopardize your entrance to the US in the future. You can find more information here.
If you have been accepted to enroll in an American college, university or institution and you wish to change your visa status from a B-1 or B-2 to a student visa (F-1 or M-1) you have to options:
1. Leave the United States and apply in your country of residence, which requires a visa interview in the US Embassy of your choice.
2. Remain in the United States and apply for a Change of Status via the United States Citizenship and Immigration Services (USCIS).
To learn about the steps you need to follow to change your status, please click here.