I know that Quicken Classic comes with access to Bill Manager which can pay bills either via electronic or physical checks mailed. Is there a way to do so with Simplifi?
No, that bill pay service is not available (yet) on Simplifi. Also, you cannot use your bank's bill pay from within Simplifi. You have to use their web login.
I actually prefer Simplifi because the bill pay module in Classic would lock payees and was just a pain to use for me.