Well, you can only file COS when you are have un-expired I-94.
If you L1B gets rejected, then you will have to leave US and then get H4 visa stamping from abroad and re-enter US, because you will be considered out of status from the day your I-94 expired, since the decision was rejected.
It should not have impact as both are different visas. You can book a date and go for H4 visa stamping.
To get H4, you will need to leave US and get visa stamping from abroad.
Read page 12 last question : [Change of Status document by USCIS ](http://www.uscis.gov/USCIS/About%20Us/Electronic%20Reading%20Room/Customer%20Service%20Reference%20Guide/NonimmigrantServices.pdf)