If you do not intend to stay in the US after you are done, than I guess it is possible. But if you want to stay, and the J-1 makes you subject to the home residency requirement, it will make things a bit more complicated later. Do you have a masters of a PhD? If so, why don't you consider applying for a self-petition green card (National Interest Waiver / Extraordinary ability) which does not require employer sponsorship or even knowledge? Can you stay at your old job until you do so? Or have you already signed a contract?
So yes, it's possible, but it's a step down because of all the restrictions and hassles of a J-1.
