A pending visa application for a different category can been seen as contradicting the purpose of your visit. In addition, most J-1 sponsoring organizations do not want you to change your status to J-1 from within the US.
It is not a good idea to try to be admitted to the U.S. with intent shortly thereafter to apply for a change of status.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
I agree with my colleagues.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
With all due respect to my colleagues, I see no problem traveling to the US on your B2 visa before it expires. Assuming, of course, that you plan on leaving the US and re-entering on the J1 in August. You might get a few extra questions when you enter in March, but as long as you are honest, I see no problem.