Voluntary employment
In my opinion, your idea about working for free elsewhere while being on J-1 is illegal and might land you in future difficulties, especially if your current J-1 sponsor is not so "co-operative." INS is reported to have recently adopted a "zero tolerance policy" for illegal immigrants. I don\'t know exactly what it eventually translates to - but be extra careful these days before touting with laws. Leave of absence to undertake other activities elsewhere can also be interpreted as intention to abandoning the J program - especially when the same person will sponor your H-1B in future thereby raising doubts over your intentions for leaves from your current program. I know one person from Turkey having done the same what you intend to. He successfully got H-1B - but his J-1 sponsor was very "co-operative." This was a case before 09/11 and before the current shake-up at the INS.
However, researchers on certain J programs are allowed to accept occasional remuneration from elsewhere if relevant to the core objectives of the program. For example, if you present results of your research during J-1 program elsewhere and deliver a lecture, you can accept the remuneration or honorarium for your talk. Check this out with your sponsor/international office.
Typically, one can expect DoS to respond within 6 to 8 weeks after they receive no objetion from the embassy. Yes, your employer can apply for your H-1B based on your DoS recommendation (I assume that the locations of your future employment and your current J program fall within the same INS jurisdiction).
Best wishes,
Jigesh
Disclaimer: Personal non-legal point of view only.