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I signed the papers electronically when i was instantly approved, card came in under 8 business days. they are usally quick I remember hearing stories a while back of longer turn around times. u should get your card soon, just get them the forms back quick.
I got my cards in about ten days. The papers to sign came too, in a separate envelope.
Both my Penfed Platinum Rewards VS and Platinum Cash Rewards cards arrived within 7-10 days, and I had to sign physical documents for both. I am fairly certain I had both cards before Penfed received the documents back. I actually had three letters to sign, including the one for membership. I believe the state you reside in may determine whether or not e-sign is available.