No you must maintain your status until 10/1 assuming you're approved for the H1B.
My answering this question does not form an attorney-client relationship. Always retain a qualified attorney before taking any action. My office offers free consultations.
You are to maintain you stay in the U.S. If you are on L-1B and even if your H-1B is approved, you will continue to maintain your status by working for L-1B employer and join H-1B employer on October 1. If things don't work out with L-1B employer and you quit, timely seek change of status or leave the U.S.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.
You must continue to maintain your status in the US.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.