A leave of 1 month is doable(of course, need some a little luck as well). I have seen both successful and unsuccessfult experience in the past. Overstay won't affect the approval theoritically. Anyway you can not get a new I-94. And you will leave and come back on H1 visa. A link to a CIS recent memo about the recapture is as follow.
http://www.uscis.gov/graphics/lawsregs/handbook/RecaptureH1BL1102105.pdf
I am luck to find a link in CIS website. Otherwise I have to paste it piecewisely.