Can my wife (dependent H4 visa) travel to India while my H1 and her H4 is still under process?

She can travel, but essentially she would be abandoning the extension petition that was submitted since she does not need that for the visa stamping. Only your H-1B extension needs to be approved for her to apply for a new H-4 visa abroad. Also, she would not be able to return until she gets the new H-4 visa and that can only happen once your H-1B is approved. Depending on how long she plans to be in India and when the H-1B would be approved would determine when she might reasonably be able to return to the US.

It is a risk for you [H-1] or your wife [H-4] to leave United States while your case is pending. If your case is denied while overseas, you'd be unable to return to the US.

If she departs the U.S. while her application for extension of H-4 is pending, her application (I-539) will be considered abandoned. I think you have a couple of options: (1) Expedite your I-129 by filing Form I-907 and paying an additional $1,225, so your wife's extension would hopefully be approved before she leaves the U.S. With an approval for H-4, she will be deemed in status from September 25, 2012 to September 25, 2015, and you'll have that much more certainty that the U.S. consulate in India will issue her a new H-4 visa.... or (2) She leaves the U.S. as planned, her application will be considered abandoned, she waits in India until your H-1B extension is approved, and then applies for her H-4. Your wife will be deemed to have been in lawful status during the time her I-539 was pending, even if ultimately not approved. In deciding between (1) and (2), you'd consider the cost of expedited processing and how long your wife needs to stay in India.