COS to F1 and H4 EAD at a time

I started my Masters in Electronics on an H4 Visa on Spring '17 and applied for COS (Form I-539) to F1 on March 7 (application received by USCIS Vermont Service centre). I got GA from one of my department professors. I checked with USCIS VSC and was informed that it will take another 3 months at the least to start processing my application. Now my husband got his I-140 approved and which gives me a chance to apply for H4 EAD. I wanted to avail benefits of OPT (which will be 3 years with STEM extension) for which I should on to F1 Visa in case approved. My Question is can I apply for H4 EAD right now so that Concurrently both the COS and H4 EAD applications can go for processing.

If YES, what happens if both of them are approved and can I choose in between them?

If NO, what would be the best option to start Fall’17 with my GA.