Someone mentioned that they have applied online and it's been more than 18 days since they haven't heard anything.
Here is a link to the post:
https://www.canadavisa.com/canada-immigration-discussion-board/threads/pr-card-application.685013/#post-8592624
I applied online today, but given the delays in almost all government procedures (landed on 16th of March and haven't received my PR yet) I suspect it will take time as well.
As for the application itself, they asked for proof of residency (COPR), proof of identity (passport) and proof of address (bank statement with printed address). They didn't ask for an email or any EE related application numbers. They did ask for my phone. I am not sure if they will communicate the SIN through phone or by mail.