No. You do not need to submit Form 3522 by mail if you already paid online to the California Franchise Tax Board.
Regarding Form 568 for a single member LLC, it must be printed and mailed, also.
See TurboTax Expert AndreaC1's answer:
TurboTax Business only handles the multi-member LLC, not single-member. If you are using
TurboTax Home & Business desktop version or Self-Employed online version, the Form 568 has to be printed and mailed.
Form 568 for single-member LLC's can't be e-filed in any of the TurboTax product versions.
The State of California’s Franchise Tax Board will allow you a waiver based on a few reasons, and due to technology constraints of the software you are using, you can request the e-file waiver.
So go here California FTB Business Entity E-file Waiver Request and request an e-file waiver so that you can paper file this form since the software version you are using won't allow e-file for it.
You will then print and mail Form 568 to this address:
FRANCHISE TAX BOARD
PO BOX 942857
SACRAMENTO CA 94257-0501
