L1 expires Jul'13. Extension applied. Can H4 application be done after expiry?

[L1toH1Query]

My L1 - I-94 expires Jul'13. My Company has applied extension already. But as L1 Extension rejection rate is very high these days and I do not want to leave country in case rejected so I want to apply H4 beforehand to safe guard my case(AND not wait for L1 extension decision). Question is : Do I need to apply the H4 COS from L1 to H4 before Jul'13 ( I-94 expiry date) or can it be applied later on as I already have a legal stay beyond Jul'13 based on my L1 Extension receipt notice.

If I have to apply L1 to H4 COS before my I-94 expiry, then is it absolute necessary to withdraw my L1 extension request? Can I withdraw my L1 extension request once my H4 is approved?( This would enable to work with my employer for few additional months).

I understand that H4 generally takes 2-3months for approval and L1 extension may take longer than that. But what will happen if L1 extension denial comes quicker before H4 approval. Then will I have to leave the country or can I stay based on my H4 application notice?