No, a pending immigrant petition for an unmarried adult child of a US Citizen (Family based-1 Classification) or married adult child of a US Citizen (Family based-3 classification) does not allow you to remain in the US legally without an underlying valid non-immigrant visa such as your current H-1B. There is a multi-year wait, shorter or longer depending upon your nationality, for immigrant visa availability under the current system based upon the priority date reflected in your I-130 Approval Notice filed by your mother.
Answered on May 14th, 2012 at 8:20 PM