You present truly case specific issues that should be legally delegated to the counsel of record who must be intimately familiar with that current case, its documents and all case developments.
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1. "Being rejected" for what? For an application for the extension of your B-1 status, to enable you to "bridge" the gap? Who knows? All depends if you'll prepare and submit a convincing application to USCIS. A denial of your EOS application should have no effect on your ability to obtain an H-1B visa stamp at a consulate abroad, once USCIS approved your employer's petition on your behalf. The reasons you are giving for wanting to remain in the US past your B-1 expiry will not be convincing for an EOS. Have to think of something better.
2. No "gap" in status is EVER fine! Overstaying by even one day could have severe consequences at the consulate later where they have absolute discretion of whether to issue your visa or not. CAnnot remain in the US out of status during the "gap" period and then expect to move on the H-1B status!
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
Chances of denial necessarily depend on sufficiency of preparation. How would we know?
You may not stay past the authorized period. All overstays can have an effect on future applications.
Dhenu Savla, Esq.
This answer does not create an attorney-client relationship and is not meant to be relied upon as legal advice.