No you can not continue to be on H1.
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The above statement is wrong.If you have not used EAD, and have a valid H1 status, even after entering back using Advanced Parole you will be in H1 status.Please look into the following dual intent memo given by INS in 2000 which clearly talks about that.Even Murthy clarrified in her chats.Please go through the links .
1)
http://www.immigrationlinks.com/news/news301.htm : Revised INM Memo on Dual Intent When Adjustment Application Pending
2)
http://www.murthy.com/chatlogs/ch082205_P.html : Murthy Clarrification
3)
http://www.immigration-law.com/Archive XI.html (Immigration-law.com clarrification look for "05/05/2005: Approaching Summer Travel Season and H-1B Traveling With Advance Parole").
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Also I understand its not your choice to use either H1 or AP... You must use your AP to reenter US once you have it.. otherwise even though you may be readmitted, it can lead to entire denial of your GC petition. It is not a chance worth taking, from what I've read and heard.
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The above statment is also not correct. It is our choice to use either H1 or AP.But if we use EAD, you will automatically loose H1.Taking AP and keepint it with us is always safe whether we use or not because, if your 485 is approved when you are abroad, you will automatically loose H1 status and you can't reenter using H1. Then only avenue is to use AP to enter.
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-Ram