At least for me, I brought the warranty card itself with my purchase receipt and I registered online as well. But they could access it from their computer and do not require me to show proof of purchase and the warranty card.
So I think if you've registered for E-warranty, it should be ok. Though it's better to bring everything unless you lost the warranty card or something .
Uuhh what you mean send back warranty card? As in hand over the warranty card to them?
For my situation, I just needed to tell them my particulars and they got my information already (Eg date of purchase, end of warranty etc etc.)
So I need not pass to them anything (except camera and equipment) for servicing.
They will pass me this "receipt" that I will need to bring along when I come to collect my stuffs. They will notify through SMS (as they claim) but I decided to call them to check if they have my stuffs with them already then I came down .
Hope this helps.
EDIT: I think I understand what you meant. Nope no need to send them your warranty card after you register for E-warranty. You can keep your actual copy of the warranty card .